Shilpa has a 4 year recurring deposit account in Bank of Maharashtra and deposits ₹800 per month. If she gets ₹48200 at the time of maturity, find

(i) the rate of (simple) interest,
(ii) the total interest earned by Shilpa

Here,
P = money deposited per month = ₹800,
n = number of months for which the money is deposited = 4 x 12 = 48

∴ Total money deposited by Shilpa = ₹(800 x 48) = ₹38400

Money Shilpa gets at the time of maturity = ₹48200

∴ Total interest earned by Shilpa = ₹48200 - ₹38400 = ₹9800

Let the rate of interest be r% per annum, then by using the formula:

$I = P \times \dfrac{n(n+1)}{2 \times 12} \times \dfrac{r}{100} \text{, we get} \\[0.7em] 9800 = \Big( 800 \times \dfrac{48 \times 49}{2 \times 12} \times \dfrac{r}{100} \Big) \\[0.5em] 9800 = 784r \\[0.5em] \Rightarrow r = \dfrac{9800}{784} \\[0.5em] \Rightarrow r = 12.5$

(i) Rate of (simple) interest = 12.5% p.a.

(ii) Total interest earned by Shilpa = ₹9800