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Q) A man has a Recurring Deposit Account in a bank for 3½ years. If the rate of interest is 12% per annum and the man gets Rs. 10,206 on maturity, find the value of monthly instalments.

Ans: Given that:

RD tenure = 3.5 years = 42 months

Rate of Interest = 12% p.a.

Maturity amount = 10,206

Step 1: Let the Monthly instalment value be P

∴ Total investment = n x P = 42 x P = 42 P

Step 2: Next, we know that Interest Amount is given by:

I = P × \frac{n (n + 1)}{2} \times \frac{r}{12 \times 100}

= P x \frac{42 (42 + 1)}{2} \times \frac{12}{12 \times 100}

= P x 21 x 43 x \frac{1}{100}

= \frac{903}{100} P

Step 3: We know that, Maturity value of RD account = Total investment + Interest Amount

∴ 10206 = 42 P + = \frac{903}{100} P

∴ 10206 x 100 = 4200 P + 903 P

∴ 10206 x 100 = 5103 P

∴ P = \frac{10206 \times 100}{5103}

∴ P = 200

Therefore, the Monthly Instalment value is Rs. 200

Check: If Monthly Instalment value is 200, then money invested over 42 months = 42 x 200 = 8400

Interest earned = P × \frac{n (n + 1)}{2} \times \frac{r}{12 \times 100}

= 200 x \frac{42 \times 43}{2} \times \frac{12}{12 \times 100} = 1806

Total maturity amount = 8400 + 1806 = 10206

Since this amount matches with given maturity amount, our answer is correct.

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