Question

Anuj took a loan of ₹50000 from a bank. If the rate of interest is 10% p.a.,find the amount he would be repaying after 1 1/2years, if the interest is:
a. compounded annually.
b. compounded half-yearly.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The amount Anuj would be repaid, after 1 1/2years, if the interest on Rs. 50000 is compounded annually is Rs. 57750 and compounded half-yearly is Rs. 57881.25 .

Step-by-step explanation:

Principal, P = Rs. 50000

Rate of interest, R = 10% p.a.

Time period, n = 1 ½  years

Let the amount he would be repaid be denoted as “A”.

Case (a): Interest is compounded annually

A = P [1 + $\frac{R}{100}$]ⁿ

Substituting the above-given values in the formula

⇒ A = 50000 [1+ $\frac{10}{100}$]^1 ½  

⇒ A = 50000 [1+$\frac{10}{100}$] [1+ $\frac{\frac{10}{2}}{100}$]

⇒ A = 50000 * $\frac{11}{10}$ * $\frac{21}{20}$

⇒ A = Rs. 57750

Thus, the amount Anuj is repaid when the interest is compounded annually is Rs. 57750.

Case (b): Interest is compounded half-yearly

Here

R = 10/2 = 5%

Time = 2n = 2 * (3/2) = 3 years

Now,

A = P [1+ $\frac{R}{100}$]²ⁿ

Substituting the above-given values in the formula

⇒ A = 50000 [1+ $\frac{5}{100}$]³  

⇒ A = 50000 * [$\frac{21}{20}$]³

⇒ A = $\frac{</strong>50000*21*21*21<strong>}{</strong>20*20*20<strong>}$

⇒ A = Rs. 57881.25

Thus, the amount Anuj is repaid when the interest is compounded half-yearly is Rs. 57881.25.

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