A man opened a recurring deposit account in a bank. He deposits ₹ 1000 per month for 2 years. The matured value is equal to 26 times the amount he pays per month. Find the :
(a) interest paid by the bank.
(b) rate of interest per annum that the bank was paying for the recurring deposit account.
Show SolutionHide Solution↓
Given,
Deposit per month (P) = ₹ 1000
Time (n) = 2 years = 24 months
Maturity value = 26 × ₹ 1000 = ₹ 26,000
(a) Total amount deposited = P × n
= 1000 × 24
= ₹ 24,000
By formula,
Interest = Maturity value − Total amount deposited
= ₹ 26,000 − ₹ 24,000
= ₹ 2,000.
Hence, interest paid by the bank = ₹ 2,000.
(b) Let the rate of interest be r% per annum.
By formula,
$I = P \times \frac{n(n + 1)}{2 \times 12} \times \frac{r}{100}$
Substituting values, we get :
$$\begin{aligned}\Rightarrow 2000 = 1000 \times \frac{24(24 + 1)}{2 \times 12} \times \frac{r}{100} \\[1em] \Rightarrow 2000 = 1000 \times \frac{24 \times 25}{24} \times \frac{r}{100} \\[1em] \Rightarrow 2000 = 1000 \times 25 \times \frac{r}{100} \\[1em] \Rightarrow 2000 = 250r \\[1em] \Rightarrow r = \frac{2000}{250} \\[1em] \Rightarrow r = 8.\end{aligned}$$
Hence, rate of interest (r%) = 8% per annum.