Anamika deposited ₹300 per month in a cumulative deposit account with a bank for 3 years. Her brother Sanjeev started depositing ₹500 per month for 2 years in the same scheme. The banks paid 10% simple interest per annum to both. At the time of maturity, find:
(a) the interest earned by Anamika.
(b) who got more money as interest and how much?
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(a) For Anamika,
P = ₹ 300, $n$ = 3 years = 36 months, $r$ = 10%
By formula,
Interest = $P \times \frac{n(n + 1)}{2 \times 12} \times \frac{r}{100}$
Substituting values we get :
$$\begin{aligned}= 300 \times \frac{36(36 + 1)}{2 \times 12} \times \frac{10}{100} \\[1em] = 300 \times \frac{36 \times 37}{24} \times \frac{10}{100} \\[1em] = 300 \times 55.5 \times \frac{10}{100} \\[1em] = 1665.\end{aligned}$$
Hence, the interest earned by Anamika = ₹ 1,665.
(b) For Sanjeev,
P = ₹ 500, $n$ = 2 years = 24 months, $r$ = 10%
By formula,
Interest = $P \times \frac{n(n + 1)}{2 \times 12} \times \frac{r}{100}$
Substituting values we get :
$$\begin{aligned}= 500 \times \frac{24(24 + 1)}{2 \times 12} \times \frac{10}{100} \\[1em] = 500 \times \frac{24 \times 25}{24} \times \frac{10}{100} \\[1em] = 500 \times 25 \times \frac{10}{100} \\[1em] = 1250.\end{aligned}$$
Interest earned by Anamika = ₹ 1,665
Interest earned by Sanjeev = ₹ 1,250
Difference = ₹ 1,665 − ₹ 1,250 = ₹ 415.
Hence, Anamika got more interest, by an amount of ₹ 415.