Question

A person sets up a sinking fund in order to have ₹ 1,00,000 after 10 years. What amount should be deposited bi-annually in the account that pays him 5% p.a. compounded semi-annually? [Given (1.025)²⁰ = 1.675]

Answer 1

Given A = ₹ 1,00,000,

Amount is deposited bi-annually for 10 years.

∴ n = 10 × 2 = 20

Rate of intererst is 5% p.a.

∴ r = ${\displaystyle \frac{5}{2}}$% = 2.5%

i = ${\displaystyle \frac{\text{r}}{100}=\frac{2.5}{100}}$ = 0.025

Now, A = ${\displaystyle \frac{\text{C}}{\text{i}}[{(1+\text{i})}^{\text{n}}-1]}$

∴ 1,00,000 = ${\displaystyle \frac{\text{C}}{0.025}[{(1+0.025)}^{20}-1]}$

∴  1,00,000 = ${\displaystyle \frac{\text{C}}{0.025}[{\left(1.025\right)}^{20}-1]}$

∴ (1,00,000)(0.025) = C[(1.025)²⁰ – 1]

∴ 2,500 = C[1.675 – 1]

∴ 2,500 = C(0.675)

∴ C = ${\displaystyle \frac{2,500}{0.675}}$ = 3,703.70

∴ Amount of ₹ 3,703.70 should be deposited bi-annualy into the account.