Question

Aman took a loan of Rs 12,000 from a bank for a period of 2 years compounded
annually. At the end of 2 years, he returned a total of Rs 15,870.
​

Answer 1

Given:

Aman took a loan of Rs 12,000 from a bank for a period of 2 years compounded annually. At the end of 2 years, he returned a total of Rs 15,870.

To find:

The rate of compound Interest at which he took the loan.​

Solution:

The sum of money, P = Rs. 12000

The no. of years, n = 2 years

The total amount received at the end of 2 years, A = Rs. 15870

Let "R%" represents the rate of compound interest

The formula of finding the amount in compound interest is:

$\boxed{\bold{A = P [1 + \frac{R}{100} ]^n}}$

Now, by using the formula above and substituting the given values, we get

$15870 = 12000 [1 + \frac{R}{100} ]^2}}$

$\implies \frac{15870}{12000} = [1 + \frac{R}{100}]^2$

$\implies 1.3225 = [1 + \frac{R}{100}]^2$

taking square root on both sides

$\implies 1.15 = [1 + \frac{R}{100}]$

$\implies 1.15 - 1 = \frac{R}{100}$

$\implies 0.15 = \frac{R}{100}$

$\implies R = 0.15 \times 100$

$\implies \bold{R =15\%}$

Thus, the rate of compound Interest at which Aman took the loan is → 15%.

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Answer 2

Given :- Aman took a loan of Rs 12,000 from a bank for a period of 2 years compounded annually. At the end of 2 years, he returned a total of Rs 15,870.

To Find :-

• Rate of interest = ?

Answer :-

Let us assume that, rate of interest is R% per annum .

So, when rate is compounded annually ,

• A = P[1 + (R/100)]ᵀ

Where,

• A = Amount .
• P = Principal .
• R = Rate of interest per annum .
• T = Time .

putting values we get,

→ 15870 = 12000[1 + (R/100)]²

→ (15870/12000) = [1 + (R/100)]²

→ (1587/1200) = [1 + (R/100)]²

→ (529/400) = [1 + (R/100)]²

→ (23/20)² = [1 + (R/100)]²

square root both sides,

→ (23/20) = 1 + (R/100)

→ (R/100) = 1 - (23/20)

→ (R/100) = (3/20)

→ R = 3 * 5

→ R = 15% per annum (Ans.)

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