A sum was invested for 3 years on compound interest at 6%, 12% and 18% in first, second and third year respectively. The sum amounts to ₹20,000 in 3 years. Find the principal amount.

Correct option is B

Given:
Amount after 3 years (A) = ₹20,000
Interest rates:
1st year: 6%
2nd year: 12%
3rd year: 18%
Formula Used:
Compound Interest Formula for varying rates:
A =$$P \times \left(1 + \frac{r_1}{100}\right) \times \left(1 + \frac{r_2}{100}\right) \times \left(1 + \frac{r_3}{100}\right)$$
Where:
P = Principal
​$$r_1, r_2, r_3$$​= Interest rates for 1st, 2nd, and 3rd years
Solution:

$$20,000 = P \times \left(1 + \frac{6}{100}\right) \times \left(1 + \frac{12}{100}\right) \times \left(1 + \frac{18}{100}\right)$$​​
20,000 = P$$\times 1.06 \times 1.12 \times 1.18$$​
P =$$\frac{20,000}{1.400896} \approx 14,276.58$$​​