Question

A sum of money becomes ₹ 5832 in 2 years and ₹ 6298.56 in 3 years, invested compounded annually. Find the rate of interest and the sum of money.

Answer 1

Given:

• Amount after 2 years = ₹ 5832
• Amount after 3 years = ₹ 6298.56
• Interest is compounded annually.

Step-wise calculation:

1. Let the principal be P and the rate of interest per annum be r %.

2. Then, after 2 years, the amount is:

`P(1 + r/100)^2 = 5832`   ...(i)

3. After 3 years, the amount is:

`P(1 + r/100)^3 = 6298.56`   ...(ii)

4. Dividing equation (ii) by (i), we get:

`(P(1 + r/100)^3)/(P(1 + r/100)^2) = 6298.56/5832`

⇒ `1 + r/100 = 6298.56/5832`

⇒ `1 + r/100 = 1.08`

5. Hence, `r/100 = 0.08`

⇒ r = 8%

6. Substituting r = 8% into equation (i):

`P xx (108/100)^2 = 5832`

⇒ `P xx (108 xx 108)/(100 xx 100) = 5832`

`P = (5832 xx 100 xx 100)/(108 xx 108)`

P = 5000