Mrs. Rao deposited ₹ 250 per month in a recurring deposit account for a period of 3 years. She received ₹ 10,110 at the time of maturity. Find:

(a) the rate of interest.

(b) how much more interest Mrs. Rao will receive if she had deposited ₹50 more per month at the same rate of interest and for the same time.

(a) Given,

Mrs. Rao deposited ₹ 250 per month in a recurring deposit account for a period of 3 years.

Total deposit = ₹ 250 × 3 × 12 = ₹ 9,000.

By formula,

Interest = Maturity value - Total deposit = ₹ 10,110 - ₹ 9,000 = ₹ 1,110.

Let rate of interest be r%.

Time (n) = 36 months

By formula,

$\text{Interest} = \dfrac{P \times n \times (n + 1)}{2 \times 12} \times \dfrac{r}{100}$

Substituting values we get :

$\Rightarrow 1110 = \dfrac{250 \times 36 \times (36 + 1)}{2 \times 12} \times \dfrac{r}{100} \\[1em] \Rightarrow 1110 = \dfrac{9000 \times 37}{24} \times \dfrac{r}{100} \\[1em] \Rightarrow 1110 = \dfrac{333000}{24} \times \dfrac{r}{100} \\[1em] \Rightarrow r = \dfrac{24 \times 1110 \times 100}{333000} \\[1em] \Rightarrow r = \dfrac{2664000}{333000} \\[1em] \Rightarrow r = 8\%.$

Hence, rate of interest = 8%.

(b) If per month ₹ 50 more is deposited, then :

P = ₹ 250 + ₹ 50 = ₹ 300.

P = ₹ 300, r = 8%, n = 36 months

By formula,

$\text{Interest} = \dfrac{P \times n \times (n + 1)}{2 \times 12} \times \dfrac{r}{100}$

Substituting values we get :

$\Rightarrow \text{Interest} = \dfrac{300 \times 36 \times (36 + 1)}{2 \times 12} \times \dfrac{8}{100} \\[1em] \Rightarrow \text{Interest} = \dfrac{10800 \times 37}{24} \times \dfrac{8}{100} \\[1em] \Rightarrow \text{Interest} = \dfrac{399600}{24} \times \dfrac{8}{100} \\[1em] \Rightarrow \text{Interest} = \dfrac{399600 \times 8}{24 \times 100} \\[1em] \Rightarrow \text{Interest} = \dfrac{3996}{3} \\[1em] \Rightarrow \text{Interest} = ₹1,332$

Additional Interest = New Interest - Old Interest

= ₹1,332 - ₹1,110

= ₹222.

Hence, Mrs. Rao would receive ₹222 more as interest if she had deposited ₹50 more per month at the same rate of interest and for the same time.