Problem Statement
Mrs. Goswami deposits ₹1,000 per month in a recurring deposit account for 3 years at 8% per annum simple interest. Find the maturity value of the account.
Verified Solution & Marking Scheme
State variables and formulas
Monthly deposit $P = ₹1,000$.
Time $n = 3 \text{ years} = 3 \times 12 = 36 \text{ months}$.
Rate of interest $r = 8\% \text{ p.a.}$
Calculate total interest earned
$$I = P \times \frac{n(n + 1)}{2 \times 12} \times \frac{r}{100}$$
$$I = 1000 \times \frac{36 \times 37}{24} \times \frac{8}{100}$$
$$\frac{36}{24} = \frac{3}{2}, \quad \frac{3}{2} \times 37 = 55.5$$
$$I = 10 \times 55.5 \times 8 = 555 \times 8 = ₹4,440$$
Compute Maturity Value (MV)
Total deposited amount $= P \times n = 1000 \times 36 = ₹36,000$.
$$\text{Maturity Value } MV = (P \times n) + I = 36000 + 4440 = ₹40,440$$