How much amount of money (in ₹) at compound interest will amount to ₹5,000 in 3 years if the rate of interest is 2% for the 1st year, 3% for the 2nd year and 4% for the 3rd year?

Correct option is C

Given:

Final Amount (A) = ₹5000

Time = 3 years

Rates:
1st year = 2%
2nd year = 3%
3rd year = 4%

Formula Used:
In compound interest with varying rates, the amount is calculated as:

​$$A = P \left(1 + \dfrac{R_1}{100}\right) \left(1 + \dfrac{R_2}{100}\right) \left(1 + \dfrac{R_3}{100}\right)$$​​

Solution:

5000 =$$P \left(1 + \dfrac{2}{100}\right)\left(1 + \dfrac{3}{100}\right)\left(1 + \dfrac{4}{100}\right)$$​

5000 =$$P \times \left(\dfrac{102}{100}\right) \times \left(\dfrac{103}{100}\right) \times \left(\dfrac{104}{100}\right)$$​​

5000 = P $$\times 1.02 \times 1.03 \times 1.04$$

P = $$\frac{5000}{1.02 \times 1.03 \times 1.04}$$​​