Radhika invested a sum of money at a compound interest of 40% per annum compounding half-yearly for 18 months. If the amount received by Radhika at the end of 18 months is ₹51,840, then what was the sum of money (in ₹) invested by Radhika?

Correct option is A

Given:

Rate of Interest = 40% p.a. (compounded half-yearly)
Time = 18 months = 1.5 years = 3 half-years
Amount (A) = ₹51,840

Formula Used:
Compound Interest formula:
A = P ×$$\left(1 + \frac{r}{100}\right)^n$$​​

Solution:

Here, r = rate per half-year =$$\frac{ 40}2$$​= 20%
A = 51840
51840 = P × $$\left(1 + \frac{20}{100}\right)^3$$​​
51840 = P ×$$(1.2)^3$$​​
51840 = P × 1.728
P = $$\frac{51840 }{ 1.728}$$​ = 30,000