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Calculate the present value investment for a future value lump sum return, based on a constant interest rate per period and compounding. This is a special instance of a present value calculation where payments = 0. The present value is the total amount that a future amount of money is worth right now.
Period commonly a period will be a year but it can be any time interval you want as long as all inputs are consistent. Future Value (FV) is the future value sum of your investment that you want to find a present value for Number of Periods (t) commonly this will be number of years but periods can be any time unit. Enter whole numbers or use decimals for partial periods such as months for example, 7.5 years is 7 yr 6 mo. Interest Rate (R) is the annual nominal interest rate or "stated rate" in percent. r = R/100, the interest rate in decimal Compounding (m) is the number of times compounding occurs per period. If a period is a year then annually=1, quarterly=4, monthly=12, daily = 365, etc. Continuous Compounding is when the frequency of compounding (m) is increased up to infinity. Enter c, C or Continuous for m. Rate (i) i = (r/m); interest rate per compounding period. Total Number of Periods (n) n = mt; is the total number of compounding periods for the life of the investment. Present Value (PV) the calculated present value of your future value amount PVIF Present Value Interest Factor that accounts for your input Number of Periods, Interest Rate and Compounding Frequency and can now be applied to other future value amounts to find the present value under the same conditions. Period Time period. Typcially a period will be a year but it can be any time interval as long as all inputs are in the same time unit. Future Value (FV) Future value of a lump sum. Number of Periods (t) Number of years or time periods. Perpetuity For a perpetual annuity t approaches infinity. For "Number of Periods (t)" enter p or perpetuity. Interest Rate (R) The annual nominal interest rate or stated rate per period, as a percentage. Compounding (m) The number of times compounding occurs per period. If a period is a year enter:• 1 for annual compounding
• 4 for quarterly compounding
• 12 for monthly compounding
• 365 for daily compounding Continuous Compounding For frequency of compounding (m) approaches infinity. For "Compounding (m)" enter c or continuous. Payment Amount (PMT) The amount of the cash flow annuity payment each period. Growth Rate (G) If this is a growing annuity, enter the growth rate per period of payments in percentage form. Payments per Period (Payment Frequency, q) How often payments are made each period. If a period is a year enter:
• 1 for annual payments
• 4 for quarterly payments
• 12 for monthly payments
• 365 for daily payments Payments at Period (Type) Specify whether payments occur at the end of each payment period (ordinary annuity, in arrears) or if payments occur at the beginning of each payment period (annuity due, in advance) Present Value (PV) The present value of any future value lump sum plus future cash flows (payments)
Present Value Formula for a Future Value:
\( PV = \dfrac{FV}{(1+\frac{r}{m})^{mt}} \)
where r=R/100 and is generally applied with r as the yearly interest rate, t the number of years and m the number of compounding intervals per year. We can reduce this to the more general
\( PV = \dfrac{FV}{(1+i)^n} \)
where i=r/m and n=mt with i the rate per compounding period and n the number of compounding periods.
When m approaches infinity, m → ∞ (continuous compounding)
\( PV = \dfrac{FV}{e^{rt}} \)
See the present value calculator for derivations of present value formulas.
Example Present Value Calculations for a Lump Sum Investment:
You want an investment to have a value of $10,000 in 2 years. The account will earn 6.25% per year compounded monthly. You want to know the value of your investment now to acheive this or, the present value of your investment account.
- Investment Value in 2 years FV = $10,000
- Interest Rate R = 6.25%, r = 0.0625
- Number of Periods (years) t = 2
- Compounding per Period (per year) m = 12
\( PV = \dfrac{\$10,000}{(1+\frac{0.0625}{12})^{12\times2}}= \$8,827.83 \)
Saving
The power of compounding grows your savings faster
3 minutes
The sooner you start to save, the more you'll earn with compound interest.
Compound interest is the interest you get on:
- the money you initially deposited, called the principal
- the interest you've already earned
For example, if you have a savings account, you'll earn interest on your initial savings and on the interest you've already earned. You get interest on your interest.
This is different to simple interest. Simple interest is paid only on the principal at the end of the period. A term deposit usually earns simple interest.
Save more with compound interest
The power of compounding helps you to save more money. The longer you save, the more interest you earn. So start as soon as you can and save regularly. You'll earn a lot more than if you try to catch up later.
For example, if you put $10,000 into a savings account with 3% interest compounded monthly:
- After five years, you'd have $11,616. You'd earn $1,616 in interest.
- After 10 years you'd have $13,494. You'd earn $3,494 in interest.
- After 20 years you'd have $18,208. You'd earn $8,208 in interest.
Compound interest formula
To calculate compound interest, use the formula:
A = P x (1 + r)n
A = ending balanceP = starting balance (or principal)r = interest rate per period as a decimal (for example, 2% becomes 0.02)
n = the number of time periods
How to calculate compound interest
To calculate how much $2,000 will earn over two years at an interest rate of 5% per year, compounded monthly:
1. Divide the annual interest rate of 5% by 12 (as interest compounds monthly) = 0.0042
2. Calculate the number of time periods (n) in months you'll be earning interest for (2 years x 12 months per year) = 24
3. Use the compound interest formula
A = $2,000 x (1+ 0.0042)24A = $2,000 x 1.106
A = $2,211.64
Lorenzo and Sophia compare the compounding effect
Lorenzo and Sophia both decide to invest $10,000 at a 5% interest rate for five years. Sophia earns interest monthly, and Lorenzo earns interest at the end of the five-year term.
After five years:
- Sophia has $12,834.
- Lorenzo has $12,500.
Sophia and Lorenzo both started with the same amount. But Sophia gets $334 more interest than Lorenzo because of the compounding effect. Because Sophia is paid interest each month, the following month she earns interest on interest.
The set is from Pie Charts. The revenues and the profits of five divisons of a company is given. Our task is to determine the profit and profit margin of some divisons which is asked in the follow up questions. With simple arithmetic calculations, you can ace this topic. Pie Chats in CAT is an important topic for CAT Exam, and we can expect a set in the CAT Data Interpretation and Logical Reasoning section in the CAT Exam
DI Pie Charts: Revenues and Profits
Total revenues are Rs. 1800 crores. Overall profit margin is 10%. The division with the largest revenue has the least profit margin but not the least profits. The division with the profit margin higher than all others generates the least profit. Exactly one division has the same profit margin as the overall Company. Company D generates more profits than Company E.
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General Solution Total revenues are Rs. 1800 crores. Overall profit margin is 10%. Overall profit is Rs. 180 crores. Exactly one division has the same profit margin as the overall Company. So, for this division, share of revenues should be equal to share of profits. Or, one of Company A or D has a profit margin of 10%.
Let us also compute absolute profit numbers – the 5 numbers are Rs. 35 crores, Rs. 40 crores, Rs. 25 crores, Rs. 30 crores and Rs. 50 crores The division with the largest revenue has the least profit margin but not the least profits. So, E has the least profit margin but not the least profits. Company D generates more profits than Company E, so Company E does not generate the least profit either. So, Company E should generate profits of Rs. 35 crores or Rs. 40 crores. Now, this is the critical statement – “The division with the profit margin higher than all others generates the least profit.�? Company C has the least revenue, and by a distance. So, chances are division C should have the highest profit margin. The least profit margin for division C should be 16.67%. Now, if the Rs. 25 crore profit were for any other division, the profit margin of that division would be less than 16.67%. This tells us that the Rs. 25 crore profit is made by division C at a profit margin of 16.67%. So, this is where we stand now.
The three missing profit numbers are Rs. 50 crores, Rs. 40 crores and Rs. 35 crores. Company E did not generate profit of Rs. 50 crores. So, the Rs. 50 crore profit number should have been seen by either B or D. If it had been D, then D would also have had a profit margin of 16.67%. But this is not possible as the question says – “The division with the profit margin higher than all others generates the least profit.�?. The above statement tells us that no company aprt from C had a profit margin of 16.67% or more. So, Company B should have seen a profit of Rs. 50 crores.
Company D generates more profit than E, so E should have seen a profit of Rs. 35 crores and D a profit of Rs. 40 crores.
Question 1: How much profit did Company A make? a. Rs. 50 crores b. Rs. 25 crores c. Rs. 30 crores d. Rs. 60 crores
Company A saw profits of Rs. 30 crores. Choice C.
We do not even need to solve the whole grid for this. The statement “Exactly one division has the same profit margin as the overall Company.�? alone is sufficient. Question 2: What was the profit margin for company B? a. 12.33% b. 8.33% c. 11.11% d. 12.5%Profit margin of B was 11.11%. Choice C
Question 3: How much profit did company E make? a. Rs. 40 crores b. Rs. 35 crores c. Rs. 50 crores d. Rs. 60 croreCompany E made Rs. 35 crore profit. Choice B
Question 4: Which company saw a profit margin of 13.33%?Company D had a profit margin of 13.33%