Question

A certain loan was returned in two equal half yearly instalments each of 6760 rupees. If the rate of intrest was 8% a compunded yearly, how much was the interest paid on the loan

Answer 1

Given:

Amount paid as half yearly installment each = Rs. 6760

Rate of interest = 8 % compounded per annum

To find:

Interest paid on the loan = ?

Solution:

Rate of interest as per half yearly installment = $\frac{8\%}{2}=4\%$

Formula for amount as per compound interest:

$A = P(1+\frac{R}{100})^T\\OR\\P = \dfrac{A}{(1+\frac{R}{100})^T}$

Using the formula for two installments:

$P = \dfrac{6760}{1+\frac{4}{100}}+\dfrac{6760}{(1+\frac{4}{100})^2}\\\Rightarrow P = \dfrac{6760\times 100}{104}+\dfrac{6760\times 10000}{(104)^2}\\\Rightarrow P = 6500 + 6250\\\Rightarrow P = 12750$

Total amount paid = 6760 + 6760 = 13520

Therefore, the interest paid = Total amount paid - Total principal = 13520 - 12750 = 770

So, the answer is:

Total interest paid = 770