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6.1 Principal, Rate, Time 6.2 Moving Money Involving Simple Interest 6.3 Savings Accounts and Short-Term GICs If you have a lot of surplus cash, it would hardly make sense to hide it under your mattress or bury it in the backyard of your townhouse. As any investment specialist will tell you, you want your money to work for you instead of just sitting idle. So you can invest and be rewarded by earning interest. Do you know if your account at the Royal Bank of Canada (RBC) has paid you the right amount of interest? You might assume that because everything at a bank is fully automated it is guaranteed to be correct. However, ultimately all automation at the Royal Bank relies on input by an employee. What if your interest rate is keyed in wrong? Maybe the computer programmer erred in a line of computer code and the amount of interest is miscalculated. What if RBC had a computer glitch? These pitfalls highlight the importance of always checking your account statements. In business, it would be rare for an organization to borrow or lend money for free. That is not to say that businesses are ruthless with each other; in the previous chapter, you saw that most business transactions are completed through interest-free credit transactions involving invoicing. However, this generosity does not extend indefinitely. After the credit period elapses, the business essentially treats an unpaid invoice as a loan and starts charging an interest penalty. When businesses need to borrow money, promissory notes, demand loans, and commercial papers are just three of the possibilities discussed later in this chapter. Even governments need to borrow money. Have you ever thought about how the government of Canada or your provincial government goes about doing that? While a government has many methods at its disposal, a common method is to use treasury bills—in essence, borrowing the money from investors. On a personal level, almost all people invest and borrow money at some time. This chapter examines consumer lines of credit and student loans, both of which carry simple interest rates. On the earnings side, it is common for people to have savings accounts that earn low rates of interest. Other short-term investments include treasury bills, commercial papers, and short-term guaranteed investment certificates (GICs). The bottom line is that money does not come free. In this chapter, you will explore the concept of simple interest, learn how to calculate it, and then apply simple interest to various financial tools. Your investments may be at risk if stock and bond markets slump, as a story in the Globe and Mail predicts. You wonder if you should shift your money into relatively secure short-term investments until the market booms again. You consider your high-interest savings account, but realize that only the first $60,000 of your savings account is insured. Perhaps you should put some of that money into treasury bills instead. Looking ahead, what income will you live on once you are no longer working? As your career develops, you need to save money to fund your lifestyle in retirement. Some day you will have $100,000 or more that you must invest and reinvest to reach your financial retirement goals. To make such decisions, you must first understand how to calculate simple interest. Second, you need to understand the characteristics of the various financial options that use simple interest. Armed with this knowledge, you can make smart financial decisions! The world of finance calculates interest in two different ways:
Simple InterestIn a simple interest environment, you calculate interest solely on the amount of money at the beginning of the transaction. When the term of the transaction ends, you add the amount of the simple interest to the initial amount. Therefore, throughout the entire transaction the amount of money placed into the account remains unchanged until the term expires. It is only on this date that the amount of money increases. Thus, an investor has more money or a borrower owes more money at the end. The figure illustrates the concept of simple interest. In this example, assume $1,000 is placed into an account with 12% simple interest for a period of 12 months. For the entire term of this transaction, the amount of money in the account always equals $1,000. During this period, interest accrues at a rate of 12%, but the interest is never placed into the account. When the transaction ends after 12 months, the $120 of interest and the initial $1,000 are then combined to total $1,120. A loan or investment always involves two parties—one giving and one receiving. No matter which party you are in the transaction, the amount of interest remains unchanged. The only difference lies in whether you are earning or paying the interest.
The FormulaThe best way to understand how simple interest is calculated is to think of the following relationship: Amount of simple interest = How much at What simple interest rate for How long Notice that the key variables are the amount, the simple interest rate, and time. Formula 6.1 combines these elements into a formula for simple interest.
How It Works Follow these steps when you calculate the amount of simple interest: Step 1: Formula 6.1 has four variables, and you need to identify three for any calculation involving simple interest. If necessary, draw a timeline to illustrate how the money is being moved over time. Step 2: Ensure that the simple interest rate and the time period are expressed with a common unit. If they are not already, you need to convert one of the two variables to the same units as the other. Step 3: Apply Formula 6.1 and solve for the unknown variable. Use algebra to manipulate the formula if necessary. Assume you have $500 earning 3% simple interest for a period of nine months. How much interest do you earn? Step 1: Note that your principal is $500, or P = $500. The interest rate is assumed to be annual, so r = 3% per year. The time period is nine months. Step 2: Convert the time period from months to years: t = Step 3: According to Formula 6.1, I = $500 × 3% × = $11.25. Therefore, the amount of interest you earn on the $500 investment over the course of nine months is $11.25. Important Notes Recall that algebraic equations require all terms to be expressed with a common unit. This principle remains true for Formula 6.1, particularly with regard to the interest rate and the time period. For example, if you have a 3% annual interest rate for nine months, then either
Paths To Success Four variables are involved in the simple interest formula, which means that any three can be known, requiring you to solve for the fourth missing variable. To reduce formula clutter, the triangle technique illustrated here helps you remember how to rearrange the formula as needed. Give It Some Thought
Solutions: 1. More, because the interest is earned and therefore is added to your savings account. 2. More, because you owe the principal and you owe the interest, which increases your total amount owing.
Time and DatesIn the examples of simple interest so far, the time period equalled an exact number of months. While this is convenient in many situations, financial institutions and organizations calculate interest based on the exact number of days in the transaction, which changes the interest amount. To illustrate this, assume you had money saved for the entire months of July and August, where t = or t = 0.1 of a year. However, if you use the exact number of days, the 31 days in July and 31 days in August total 62 days. In a 365-day year that is t = %or t = 0.169863 of a year. Notice a difference of 0.003196 occurs. Therefore, to be precise in performing simple interest calculations, you must calculate the exact number of days involved in the transaction. Figuring Out the Days In practice, when counting the number of days in a transaction you include the first day but not the last day. This is because interest is calculated on the daily closing balance, not on interim balances throughout a day. For example, if you borrowed $500 on June 3 and paid it back with interest on June 5, the closing balance on June 3 and June 4 is $500. However, on June 5 a zero balance is restored. Therefore, you count June 3 and 4 as days of interest but not June 5, so you will owe two days of interest, not three. There are three common ways to calculate the number of days involved in a transaction. Method 1: Use Your Knuckles You can use your knuckles as an aid to remembering which months of the year have more or fewer days. Put your knuckles side by side and start on your outermost knuckle. Every knuckle represents a month with 31 days. Every valley between the knuckles represents a month that does not have 31 days (30 in all except February, which has 28 or 29). Now start counting months. Your first knuckle (pinkie finger) is January, which has 31 days. Next is your first valley, which is February and it does not have 31 days. Your next knuckle (ring finger) is March, which has 31 days … and so on. When you get to your last knuckle (your index finger), move to the other hand’s first knuckle (an index finger again). Notice that July and August are the two months back to back with 31 days. If you are trying to calculate the number of days between March 20 and May 4, use your knuckles to recall that March has 31 days and April has 30 days. The calculations are illustrated in the table here.
Why does the end date of one line become the start date of the next line? Recall that you count the first day, but not the last day. Therefore, on the first line March 31 has not been counted yet and must be counted on the second line. Ultimately a transaction extending from March 20 to May 4 involves 45 days as the time period. Method 2: Use A Table of Serial Numbers In the table on the next page, the days of the year are assigned a serial number. The number of days between any two dates in the same calendar year is simply the difference between the serial numbers for the dates. Using the example in Method 1, when the dates are within the same calendar year, find the serial number for the later date, May 4 (Day 124) and the serial number for the earlier date, March 20 (Day 79). Then, find the difference between the two serial numbers (124 – 79 = 45 days). *For Leap years, February 29 becomes Day 60 and the serial number for each subsequent day is increased by 1. Method 3: Use The BAII Plus Date Function Your BAII Plus calculator is programmed with the ability to calculate the number of days involved in a transaction according to the principle of counting the first day but not the last day. The function “Date” is located on the second shelf above the number one. To use this function, open the window by pressing 2nd 1.
4. ACT or 360 is the method of calculating the days between dates. In ACT (for “actual”), the calculator calculates the DBD based on the correct number of days in the month. In 360, the DBD is based on treating every month as having 30 days (30 × 12 = 360 days). For all calculations, set the calculator to the ACT mode. Toggle this setting by pressing 2nd SET.
Using the example in Method 1, to calculate the time from March 20 to May 4 you first need to choose a year arbitrarily, perhaps 2011. Therefore, perform the following sequence: 2nd DATE 2nd CLR Work (to erase previous calculations) 3.2011 ENTER ↓ (this is March 20, 2011) 5.0411 ENTER ↓ (this is May 4, 2011) CPT Answer: 45 Note that the answer is the same as the one you arrived at manually using your knuckles. Important Notes When solving for t, decimals may appear in your solution. For example, if calculating t in days, the answer may show up as 45.9978 or 46.0023 days; however, interest is calculated only on complete days. This occurs because the interest amount (I) used in the calculation has been rounded off to two decimals. Since the interest amount is imprecise, the calculation of t is imprecise. When this occurs, round t off to the nearest integer. Things To Watch Out For Miscalculating the number of days in February has to be one of the most common errors. To help you remember how many days are in February, recall your knowledge of leap years.
Note that when it comes to the total number of days in a year, simple interest calculations ignore the 366th day in a leap year. Therefore, assume a year has 365 days in all calculations. Paths To Success When entering two dates either on the calculator or in Excel, the order in which you key in the dates is not important. If you happen to put the last day of the transaction into the first field (DT1 or Start Date) and the start day of the transaction into the last field (DT2 or End Date), then the number of days will compute as a negative number since the dates are reversed. Ignore the negative sign in these instances. Using the example, on your calculator if you had keyed May 4 into DT1 and March 20 into DT2, the DBD computes as −45, in which you ignore the negative sign to determine the answer is 45 days.
Variable Interest RatesNot all interest rates remain constant. There are two types of interest rates:
In all of the previous examples in this section, the interest rate (r) was fixed for the duration of the transaction. When r fluctuates, you must break the question into time periods or time fragments for each value of r. In each of these time fragments, you calculate the amount of simple interest earned or charged and then sum the interest amounts to form the total interest earned or charged. This figure illustrates this process with a variable rate that changes twice in the course of the transaction. To calculate the total interest amount, you need to execute Formula 6.1 for each of the time fragments. Then total the interest amounts from each of the three time fragments to calculate the interest amount (I) for the entire transaction.
For each of the following questions, round all money to two decimals and percentages to four decimals. Mechanics For questions 1–6, solve for the unknown variables (identified with a ?) based on the information provided.
Applications
Challenge, Critical Thinking, & Other Applications
What percentage more interest is earned in the best alternative versus the worst alternative? Can you calculate the amount of money required to meet a future goal? Assume you will graduate college with your business administration diploma in a few months and have already registered at your local university to continue with your studies toward a bachelor of commerce degree. You estimate your total tuition, fees, and textbooks at $8,000. After investigating some short-term investments, you find the best simple rate of interest obtainable is 4.5%. How much money must you invest today for it to grow with interest to the needed tuition money? In the previous section, you calculated the amount of interest earned or charged on an investment or loan. While this number is good to know, most of the time investors are interested solely in how much in total, including both principal and interest, is either owed or saved. Also, to calculate the interest amount in Formula 6.1, you must know the principal. When people plan for the future, they know the future amount of money that they need but do not know how much money they must invest today to arrive at that goal. This is the case in the opening example above, so you need a further technique for handling simple interest. This section explores how to calculate the principal and interest together in a single calculation. It adds the flexibility of figuring out how much money there is at the beginning of the time period so long as you know the value at the end, or vice versa. In this way, you can solve almost any simple interest situation. Maturity Value (or Future Value)The maturity value of a transaction is the amount of money resulting at the end of a transaction, an amount that includes both the interest and the principal together. It is called a maturity value because in the financial world the termination of a financial transaction is known as the “maturing” of the transaction. The amount of principal with interest at some point in the future, but not necessarily the end of the transaction, is known as the future value.
Depending on the financial scenario, what information you know, and what variable you need to calculate, you may need a second formula offering an alternative method of calculating the simple interest dollar amount.
How It Works Follow these steps when working with single payments involving simple interest: Step 1: Formula 6.2 has four variables, any three of which you must identify to work with a single payment involving simple interest.
Step 2: Ensure that the simple interest rate and the time period are expressed with a common unit. If not, you need to convert one of the two variables to achieve the commonality. Step 3: Apply Formula 6.2 and solve for the unknown variable, manipulating the formula as required. Step 4: If you need to calculate the amount of interest, apply Formula 6.3. Assume that today you have $10,000 that you are going to invest at 7% simple interest for 11 months. How much money will you have in total at the end of the 11 months? How much interest do you earn? Step 1: The principal is P = $10,000, the simple interest rate is 7% per year, or r = 0.07, and the time is t = 11 months. Step 2: The time is in months, but to match the rate it needs to be expressed annually as t = Step 3: Applying Formula 6.2 to calculate the future value including interest, S = $10,000 × (1 + 0.07 × ) = $10,641.67. This is the total amount after 11 months. Step 4: Applying Formula 6.3 to calculate the interest earned, I = $10,641.67 − $10,000.00 = $641.67. You could also apply Formula 6.1 to calculate the interest amount; however, Formula 6.3 is a lot easier to use. The $10,000 earns $641.67 in simple interest over the next 11 months, resulting in $10,641.67 altogether. Things To Watch Out For As with Formula 6.1, the most common mistake in the application of Formula 6.2 is failing to ensure that the rate and time are expressed in the same units. Before you proceed, always check these two variables! Paths To Success When solving Formula 6.2 for either rate or time, it is generally easier to use Formulas 6.3 and 6.1 instead. Follow these steps to solve for rate or time:
Give It Some Thought In each of the following situations, determine which statement is correct.
Equivalent PaymentsLife happens. Sometimes the best laid financial plans go unfulfilled. Perhaps you have lost your job. Maybe a reckless driver totalled your vehicle, which you now have to replace at an expense you must struggle to fit into your budget. No matter the reason, you find yourself unable to make your debt payment as promised. On the positive side, maybe you just received a large inheritance unexpectedly. What if you bought a scratch ticket and just won $25,000? Now that you have the money, you might want to pay off that debt early. Can it be done? Whether paying late or paying early, any amount paid must be equivalent to the original financial obligation. As you have learned, when you move money into the future it accumulates simple interest. When you move money into the past, simple interest must be removed from the money. This principle applies both to early and late payments:
Notice in these examples that a simple interest rate of 10% means $100 today is the same thing as having $110 one year from now. This illustrates the concept that two payments are equivalent payments if, once a fair rate of interest is factored in, they have the same value on the same day. Thus, in general you are finding two amounts at different points in time that have the same value, as illustrated in the figure below.
How It Works The steps required to calculate an equivalent payment are no different from those for single payments. If an early payment is being made, then you know the future value, so you solve for the present value (which removes the interest). If a late payment is being made, then you know the present value, so you solve for the future value (which adds the interest penalty). Paths To Success Being financially smart means paying attention to when you make your debt payments. If you receive no financial benefit for making an early payment, then why make it? The prudent choice is to keep the money yourself, invest it at the best interest rate possible, and pay the debt off when it comes due. Whatever interest is earned is yours to keep and you still fulfill your debt obligations in a timely manner!
For each of the following questions, round all money to two decimals and percentages to four decimals. Mechanics For questions 1–4, solve for the unknown variables (identified with a ?) based on the information provided.
Questions 5–8 involve either early or late payments. Calculate the following for each:
Applications
Challenge, Critical Thinking, & Other Applications
How much did Alia originally invest on March 2? Assume that the principal and interest from a prior investment are both placed into the next investment.
When the stock market offers potentially huge returns, why would anyone put money into an investment that earns just a few percent annually? The answer of course is that sometimes stocks decrease in value. For example, after reaching a historic high in June 2008, the Toronto Stock Exchange plunged 40% over the course of the next six months. So if you are not willing to take the risk in the stock market, there are many options for investing your money that are safe and secure, particularly savings accounts and short-term guaranteed investment certificates (GICs). Some of the benefits and drawbacks associated with safe and secure investments are listed in the table below.
Savings AccountsA savings account is a deposit account that bears interest and has no stated maturity date. These accounts are found at most financial institutions, such as commercial banks (Royal Bank of Canada, TD Canada Trust, etc.), trusts (Royal Trust, Laurentian Trust, etc.), and credit unions (FirstOntario, Steinbach, Assiniboine, Servus, etc.). Owners of such accounts make deposits to and withdrawals from these accounts at any time, usually accessing the account at an automatic teller machine (ATM), at a bank teller, or through online banking. A wide variety of types of savings accounts are available. This textbook focuses on the most common features of most savings accounts, including how interest is calculated, when interest is deposited, insurance against loss, and the interest rate amounts available.
While a wide range of savings accounts are available, these accounts generally follow one of two common structures when it comes to calculating interest. These structures are flat rate savings accounts and tiered savings accounts. Each of these is discussed separately.
How It Works Flat-Rate Savings Accounts. A flat-rate savings account has a single interest rate that applies to the entire balance. The interest rate may fluctuate in synch with short-term interest rates in the financial markets. Follow these steps to calculate the monthly interest for a flat-rate savings account: Step 1: Identify the interest rate, opening balance, and the monthly transactions in the savings account. Step 2: Set up a flat-rate table as illustrated here. Create a number of rows equalling the number of monthly transactions (deposits or withdrawals) in the account plus one.
Step 3: For each row of the table, set up the date ranges for each transaction and calculate the balance in the account for each date range. Step 4: Calculate the number of days that the closing balance is maintained for each row. Step 5: Apply Formula 6.1, I = Prt, to each row in the table. Ensure that rate and time are expressed in the same units. Do not round off the resulting interest amounts (I). Step 6: Sum the Simple Interest Earned column and round off to two decimals. When you are calculating interest on any type of savings account, pay careful attention to the details on how interest is calculated and any restrictions or conditions on the balance that is eligible to earn the interest.
How It Works Tiered Savings Accounts. A tiered savings account pays higher rates of interest on higher balances in the account. This is very much like a graduated commission on gross earnings, as discussed in Section 4.1. For example, you might earn 0.25% interest on the first $1,000 in your account and 0.35% for balances over $1,000. Most of these tiered savings accounts use a portioning system. This means that if the account has $2,500, the first $1,000 earns the 0.25% interest rate and it is only the portion above the first $1,000 (hence, $1,500) that earns the higher interest rate. Follow these steps to calculate the monthly interest for a tiered savings account: Step 1: Identify the interest rate, opening balance, and the monthly transactions in the savings account. Step 2: Set up a tiered interest rate table as illustrated below. Create a number of rows equalling the number of monthly transactions (deposits or withdrawals) in the account plus one. Adjust the number of columns to suit the number of tiered rates. Fill in the headers for each tiered rate with the balance requirements and interest rate for which the balance is eligible.
Step 3: For each row of the table, set up the date ranges for each transaction and calculate the balance in the account for each date range. Step 4: For each row, calculate the number of days that the closing balance is maintained. Step 5: Assign the closing balance to the different tiers, paying attention to whether portioning is being used. In each cell with a balance, apply Formula 6.1, where I = Prt. Ensure that rate and time are expressed in the same units. Do not round off the resulting interest amounts (I). Step 6: To calculate the Total Monthly Interest Earned, sum all interest earned amounts from all tier columns and round off to two decimals.
The Rate Builder savings account at your local credit union pays simple interest on the daily closing balance as indicated in the table below:
Short-Term Guaranteed Investment Certificates (GICs)A guaranteed investment certificate (GIC) is an investment that offers a guaranteed rate of interest over a fixed period of time. In many countries around the world, a GIC is often called a time or term deposit. GICs are found mostly at commercial banks, trust companies, and credit unions. Just like savings accounts, they have a very low risk profile and tend to have much lower rates than are available through other investments such as the stock market or bonds. They are also unconditionally guaranteed, much like savings accounts. In this section, you will deal only with short-term GICs, defined as those that have a time frame of less than one year. The table below summarizes three factors that determine the interest rate on a short-term GIC: principal, time, and redemption privileges.
Amount of Principal. Typically, a larger principal is able to realize a higher interest rate than a smaller principal.
Mechanics
Applications
The opening balance in February of a non–leap year was $47,335. The transactions on this account were a deposit of $60,000 on February 8, a withdrawal of $86,000 on February 15, and a deposit of $34,000 on February 24. What interest for the month of February will be deposited to the account on March 1?
December’s opening balance was $550,000. Two deposits in the amount of $600,000 each were made on December 3 and December 21. Two withdrawals in the amount of $400,000 and $300,000 were made on December 13 and December 24, respectively. What interest for the month of December will be deposited to the account on January 1?
Challenge, Critical Thinking, & Other Applications
For any given month, simple interest is calculated on the lowest monthly closing balance, but the interest is not deposited until January 1 of the following year. On January 1, 2014, the opening balance on an account was $75,000. The following transactions took place throughout the year:
Calculate the annual amount of interest earned on this account that will be deposited on January 1, 2015. Interest rates can fluctuate throughout the year. Working with the information from question 11, recalculate the annual amount of interest if all of the posted interest rates were adjusted as follows throughout the year:
13. Interest rates in the GIC markets are always fluctuating because of changes in the short-term financial markets. If you have $50,000 to invest today, you could place the money into a 180-day GIC at Canada Life earning a fixed rate of 0.4%, or you could take two consecutive 90-day GICs. The current posted fixed rate on 90-day GICs at Canada Life is 0.3%. Trends in the short-term financial markets suggest that within the next 90 days short-term GIC rates will be rising. What does the short-term 90-day rate need to be 90 days from now to arrive at the same maturity value as the 180-day GIC? Assume that the entire maturity value of the first 90-day GIC would be reinvested. 14. A Citibank Savings Account posts the following simple interest rate structure. All interest is paid on entire balances, and interest is deposited to the account every quarter.
On January 1, 2013, the opening balance was $3,300. The following transactions took place during the first quarter (January 1 to March 31):
Calculate the total amount of interest that will be deposited to the account on April 1, 2013.
In all cases, assume that the posted rates remain unchanged and that the entire maturity value will be reinvested in the next short-term GIC. Calculate the total maturity value for each option at the end of 360 days.
accrued interest Any interest amount that has been calculated but not yet placed (charged or earned) into an account. commercial paper A short-term financial instrument with maturity no longer than one year that is issued by large corporations. compound interest A system for calculating interest that primarily applies to long-term financial transactions with a time frame of one year or more; interest is periodically converted to principal throughout a transaction, with the result that the interest itself also accumulates interest. current balance The balance in an account plus any accrued interest. demand loan A short-term loan that generally has no specific maturity date, may be paid at any time without any interest penalty, and where the lender may demand repayment at any time. discount rate An interest rate used to remove interest from a future value. equivalent payments Two payments that have the same value on the same day factoring in a fair interest rate. face value of a T-bill The maturity value of a T-bill, which ispayable at the end of the term. It includes both the principal and interest together. fixed interest rate An interest rate that is unchanged for the duration of the transaction. future value The amount of principal with interest at a future point of time for a financial transaction. If this future point is the same as the end date of the financial transaction, it is also called the maturity value. guaranteed investment certificate (GIC) An investment that offers a guaranteed rate of interest over a fixed period of time. interest amount The dollar amount of interest that is paid or earned. interest rate The rate of interest that is charged or earned during a specified time period. legal due date of a note Three days after the term specified in an interest-bearing promissory note is the date when a promissory note becomes legally due. This grace period allows the borrower to repay the note without penalty in the event that the due date falls on a statutory holiday or weekend. maturity date The date upon which a transaction, such as a promissory note, comes to an end and needs to be repaid. maturity value The amount of money at the end of a transaction, which includes both the interest and the principal together. present value The amount of money at the beginning of a time period in a transaction. If this is in fact the amount at the start of the financial transaction, it is also called the principal. Or it can simply be the amount at some time earlier before the future value was known. In any case, the amount excludes the interest. prime rate An interest rate set by the Bank of Canada that usually forms the lowest lending rate for the most secure loans. principal The original amount of money that is borrowed or invested in a financial transaction. proceeds The amount of money received from a sale. promissory note An unconditional promise in writing made by one person to another person to pay a sum of money on demand or at a fixed or determinable future time. repayment schedule A table that details the financial transactions in an account, including the balance, interest amounts, and payments. savings account A deposit account that bears interest and has no stated maturity date. secured loan Those loans that are guaranteed by an asset such as a building or a vehicle that can be seized to pay the debt in case of default. simple interest A system for calculating interest that primarily applies to short-term financial transactions with a time frame of less than one year. student loan A special type of loan designed to help students pay for the costs of tuition, books, and living expenses while pursuing postsecondary education. time period The length of the financial transaction for which interest is charged or earned. It may also be called the term. treasury bills Short-term financial instruments with maturities no longer than one year that are issued by both federal and provincial governments. unsecured loan Those loans backed up by the general goodwill and nature of the borrower. variable interest rate An interest rate that is open to fluctuations over the duration of a transaction. yield The percentage increase between the sale price and redemption price on an investment such as a T-bill or commercial paper. The Formulas You Need to Know Symbols Used S = maturity value or future value in dollars I = interest amount in dollars P = principal or present value in dollars r = interest rate (in decimal format) t = time or term Formulas Introduced Formula 6.1 Simple Interest: I = Prt (Section 6.1) Formula 6.2 Simple Interest for Single Payments: S = P(1 + rt) (Section 6.2) Formula 6.3 Interest Amount for Single Payments: I = S − P (Section 6.2) Technology Calculator The following calculator functions were introduced in this chapter: Date Function
Mechanics
Applications
BOS Designer Candles Inc. has an opening balance in July of $17,500. Three deposits in the amounts of $6,000, $4,000, and $1,500 were made on July 4, July 18, and July 22, respectively. Two withdrawals in the amount of $20,000 and $8,000 were made on July 20 and July 27, respectively. What interest for the month of July will Alterna deposit to the account on August 1?
Challenge, Critical Thinking, & Other Applications
On August 1, the opening balance was $6,400. Three deposits of $2,000, $3,500, and $1,500 were made on August 3, August 10, and August 27, respectively. Two withdrawals of $7,000 and $1,900 were made on August 6 and August 21, respectively. Compute the total interest earned for the month of August.
Managing A Company’s Investments The Situation As with most mid-size to large companies, Lightning Wholesale has a finance department to manage its money. The structure of Lightning Wholesale’s financial plan allows each department to have its own bank account from which all expenses, purchases, and charges are deducted. This same account has all revenues and interest deposited into it. The manager of the sporting goods department wants a summary of all interest amounts earned or charged to her department for the year 2013. This will allow her to better understand and assess the financial policies of the company and make any necessary changes for 2014. The Data
(All numbers in thousands of dollars) Important Information
Your Tasks The manager wants a report that summarizes the following information from December 31, 2012, to December 31, 2013:
In order to meet the manager’s requirements, work through 2013 month by month starting from December 31, 2012, by following the steps below. Once arriving at December 31, 2013, use the answers to provide the four pieces of information requested by the manager.
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