A sum of x amounts to Rs. 75867 in $$2\frac {1}{2}$$​ years at 12% p.a., interest compounded after every 10 months. What is the value of x?

Correct option is D

Given:
Amount (A) = Rs. 75,867
Time = 2½ years = 30 months
Rate of interest = 12% per annum
Interest is compounded after every 10 months
Formula Used:
​$$A = P (1 +\frac{R}{100})^n$$​​
Solution:
Compounding period = 10 months
Number of compounding periods=$$\frac{30}{10}$$​= 3
Rate per compounding period= 12% × $$\frac{10}{12}$$​= 10%
Substituting values in the formula:
​$$75867 = x\left(1 + \frac{10}{100}\right)^3 \\\ \\75867 = x(1.1)^3\\\ \\75867 = x \times 1.331\\\ \\x = \frac{75867}{1.331}\\\ \\x = 57{,}000$$​​