Compute the amount and the compound interest when principal = rs 3000, rate = 18%, time = 2 years.

Question:

Compute the amount and the compound interest in each of the following by using the formulae when:

(i) Principal = Rs 3000, Rate = 5%, Time = 2 years

(ii) Principal = Rs 3000, Rate = 18%, Time = 2 years

(iii) Principal = Rs 5000, Rate = 10 paise per rupee per annum, Time = 2 years

(iv) Principal = Rs 2000, Rate = 4 paise per rupee per annum, Time = 3 years

(v) Principal = Rs 12800 , Rate $=7 \frac{1}{2} \%$, Time $=3$ years

(vi) Principal = Rs 10000, Rate 20% per annum compounded half-yearly, Time = 2 years

(vii) Principal = Rs 160000, Rate = 10 paise per rupee per annum compounded half-yearly, Time = 2 years.

Solution:

Applying the rule $\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}$ on the given situations, we get:

(i)

$\mathrm{A}=3,000\left(1+\frac{5}{100}\right)^{2}$

$=3,000(1.05)^{2}$

$=\mathrm{Rs} 3,307.50$

Now,

$\mathrm{CI}=\mathrm{A}-\mathrm{P}$

$=\mathrm{Rs} 3,307.50-\mathrm{Rs} 3,000$

$=\mathrm{Rs} 307.50$

(ii)

$\mathrm{A}=3,000\left(1+\frac{18}{100}\right)^{2}$

$=3,000(1.18)^{2}$

$=\mathrm{Rs} 4,177.20$

Now,

$\mathrm{CI}=\mathrm{A}-\mathrm{P}$

$=\mathrm{Rs} 4,177.20-\mathrm{Rs} 3,000$

$=\mathrm{Rs} 1,177.20$

(iii)

$\mathrm{A}=5,000\left(1+\frac{10}{100}\right)^{2}$

$=5,000(1.10)^{2}$

$=\mathrm{Rs} 6,050$

Now,

$\mathrm{CI}=\mathrm{A}-\mathrm{P}$

$=\mathrm{Rs} 6,050-\mathrm{Rs} 5,000$

$\mathrm{CI}=\mathrm{A}-\mathrm{P}$

$=\mathrm{Rs} 6,050-\mathrm{Rs} 5,000$

$=\mathrm{Rs} 1,050$

(iv)

$\mathrm{A}=2,000\left(1+\frac{4}{100}\right)^{3}$

$=2,000(1.04)^{3}$

$=\mathrm{Rs} 2,249.68$

Now,

$\mathrm{CI}=\mathrm{A}-\mathrm{P}$

$=\mathrm{Rs} 2,249.68-\mathrm{Rs} 2,000$

$=\mathrm{Rs} 249.68$

(v)

$\mathrm{A}=12,800\left(1+\frac{7.5}{100}\right)^{3}$

$=12,800(1.075)^{3}$

$=\mathrm{Rs} 15,901.40$

Now,

$\mathrm{CI}=\mathrm{A}-\mathrm{P}$

$=\mathrm{Rs} 15,901.40-\mathrm{Rs} 12,800$

$=\mathrm{Rs} 3,101.40$

(vi)

$\mathrm{A}=10,000\left(1+\frac{20}{200}\right)^{4}$

$=10,000(1.1)^{4}$

$=\mathrm{Rs} 14,641$

Now,

$\mathrm{CI}=\mathrm{A}-\mathrm{P}$

$=\mathrm{Rs} 14,641-\mathrm{Rs} 10,000$

$=\mathrm{Rs} 4,641$

(vii)

$\mathrm{A}=16,000\left(1+\frac{10}{200}\right)^{4}$

$=16,000(1.05)^{4}$

$=\mathrm{Rs} 19,448.1$

Now,

$\mathrm{CI}=\mathrm{A}-\mathrm{P}$

$=\mathrm{Rs} 19,448.1-\mathrm{Rs} 16,000$

$=\mathrm{Rs} 3,448.1$

By using the formula,

A = P (1 + R/100)^n

Let us solve

(i)Given, P = Rs 3000, rate = 5%, time = 2years

A = P (1 + R/100)^n

= 3000 (1 + 5/100)^2

= 3000 (105/100)^2

= Rs 3307.5

Compound interest (CI) = A-P = Rs 3307.5 – 3000 = Rs 307.5

(ii)Given, P = Rs 3000, rate = 18%, time = 2years

A = P (1 + R/100)^n

= 3000 (1 + 18/100)^2

= 3000 (118/100)^2

= Rs 4177.2

Compound interest (CI) = A-P = Rs 4177.2 – 3000 = Rs 1177.2

(iii)Given, P = Rs 5000, rate = 10%, time = 2years

A = P (1 + R/100)^n

= 5000 (1 + 10/100)^2

= 5000 (110/100)^2

= Rs 6050

Compound interest (CI) = A-P = Rs 6050 – 5000 = Rs 1050

(iv)Given, P = Rs 2000, rate = 4%, time = 3years

A = P (1 + R/100)^n

= 2000 (1 + 4/100)^3

= 2000 (104/100)^3

= Rs 2249.72

Compound interest (CI) = A-P = Rs 2249.72 – 2000 = Rs 249.72

(v)Given, P = Rs 12800, rate = 7 ½ % = 15/2% = 7.5%, time = 3years

A = P (1 + R/100)^n

= 12800 (1 + 7.5/100)^3

= 12800 (107.5/100)^3

= Rs 15901.4

Compound interest (CI) = A-P = Rs 15901.4 – 12800 = Rs 3101.4

(vi)Given, P = Rs 10000, rate = 20 % = 20/2 = 10% (quarterly), time = 2years = 2 × 2 =4years

A = P (1 + R/100)^n

= 10000 (1 + 10/100)^4

= 10000 (110/100)^4

= Rs 14641

Compound interest (CI) = A-P = Rs 14641 – 10000 = Rs 4641

(vii)Given, P = Rs 160000, rate = 10% = 10/2% = 5% (half yearly), time = 2years = 2×2

= 4 quarters

A = P (1 + R/100)^n

= 160000 (1 + 5/100)^4

= 160000 (105/100)^4

= Rs 194481

Compound interest (CI) = A-P = Rs 194481 – 160000 = Rs 34481

Question 1 Compound Interest Exercise 14.1

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Answer:

Given details are,

Principal (p) = Rs 3000

Rate (r) = 5%

Time = 2years

Interest for the first year = (3000×5×1)/100 = 150

Amount at the end of first year = Rs 3000 + 300 = Rs 3150

Principal interest for the second year = (3150×5×1)/100 = 157.5

Amount at the end of second year = Rs 3150 + 157.5 = Rs 3307.5

∴ Compound Interest = Rs 3307.5 – Rs 3000 = Rs 307.5

Video transcript

"hello students welcome to lido's question and answer classroom my name is shaista ferrosi class and today we are going to find out the compound interest okay so let's start with the question first as you can see find the compound interest when principal is rupees three thousand so here you can see that principle is given as three thousand rate is five percent per annum and time is two years okay so let's quickly jot down whatever information is given to us so uh i need i have principle which is equals to rupees 3000 my rate which is equals to five percent and the time okay so time is given as two years okay now here you need to find out the compound interest as you all know that the compound interest formula is equals to amount minus principle but we need for this amount now since uh if you have noticed over here that we required it for two years okay so we require the compound interest for two years so before that what i will go i am going to do is i am going to find out the amount of every first year so after every first year i am going to find out the amount so let us first find out the interest okay so interest for the first year just hold okay so my interest for the first year okay so i'm just writing first here will be equal to p into r into t that's the formula upon hundred so my principle as you can see is three thousand into rate of interest which is equal to 5 into time period i'm going to take it as 1 because i'm going to calculate the interest for two years differently okay so i'm taking it for the first year now then again i will take it for one more year so let's write down this and on calculation i am going to write i'm going to uh get my 150 rupees okay so here you can see that i have got my interest for the first year as rupees 150 now i am going to find out the amount for this so let's quickly find out the amount at the end of the first year so at the end of the first year i am going to take as principal plus interest which is equals to by principal is 3000 my interest as you know that we got as rupees 150 so my amount is equals to 3150 rupees so this is my amount at the end of the first year now since i got the amount at the end of the first error is this i am going to find out the amount for the second year but before that please do remember since this is my amount i am going to take it for the second year i am going to take this as my principal amount so let's write down the principal interest i would say rather so my interest or principal interest you can say for the second year would be p into r into t please do remember the principle will be this only because it will be for the first year i'm going to take it for the second year the amount will be my principle new principle so principle would be three thousand one hundred and fifty into rate of interest is five time is one again i'm since i'm taking it one year because it is for the second year i'm calculating so i am going to take this as one on calculation i am going to get and 1570 five point five okay so since i got this as the interest for the first second here now we will going we will quickly find out the amount at the second year so my amount for the second year would be again principal plus interest as you know that principle i have taken it as 3150 plus my interest which came to be 157.5 my answer would be rupees 333rd three thousand three hundred and seven point five okay so okay so here you can see that i have got my amount i have got my amount for the second year as this and amount for the first year as this okay so now i can find out easily my compound interest would be amount which is nothing but 3307 because i had taken i am not going to consider this amount because i have already taken this as a principle for the second year so i'm just considering this amount minus the principle which was the actual principle which is 3000 and therefore my compound interest is rupees 307.5 so therefore you can see that we got our compound interest after two years would be 307.5 hope this much is clear all right that's all for today see you all next time bye "

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