A sum of Rs.P was borrowed and paid back in two equal yearly instalments, each of Rs.35,280. If the rate of interest was 5% per annum and interest is compounding annually, then the value of P is ________.

Correct option is B

Given:
Principal = P (to be found)
Rate of Interest = 5% per annum (compounded annually)
Two equal yearly instalments = Rs. 35,280 each
Formula Used:
​$$\text{Present Value} = \frac{A}{(1+r)^1} + \frac{A}{(1+r)^2}$$​​
Solution:
$$P = \frac{35,280}{(1 + \tfrac{5}{100})} + \frac{35,280}{(1 + \tfrac{5}{100})^2} \\[6pt]\Rightarrow P = \frac{35,280}{(1 + \tfrac{1}{20})} + \frac{35,280}{(1 + \tfrac{1}{20})^2} \\[6pt]\Rightarrow P = \frac{35,280}{(21/20)} + \frac{35,280}{(21/20)^2} \\[6pt]\Rightarrow P = 35,280 \times \frac{20}{21} + 35,280 \times \frac{400}{441} \\[6pt]\Rightarrow P = 35,280 \times \frac{20}{21} \bigl[1 + \tfrac{20}{21}\bigr] \\[6pt]\Rightarrow P = 35,280 \times \frac{20}{21} \times \frac{41}{21} \\[6pt]\Rightarrow P = 65,600$$​​