Question

Find the rate of interest compounded annually if an immediate annuity of ₹ 20,000 per year amounts to ₹ 41,000 in 2 years.

Answer 1

Here, C = ₹ 20,000, A = ₹ 41,000, n = 2

`A = C/i[(1 + i)^n - 1`

∴ `41,000 = (20,000)/i [(1 + i)^2 - 1]`

∴ `(41,000)/(20,000) = 1/i [(1 + i)^2 - 1]`

∴ `2.05 = 1/i (1 + 2i + i^2 - 1)`

∴ `2.05 = 1/i (2i + i^2)`

∴ 2.05 = 2 + i

∴ i = 0.05

But `i = r/100`

∴ `0.05 = r/100`

∴ r = 0.05 × 100

= 5%

Hence, the rate of interest is 5%.