Question

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:

1. the rate of interest. 
2. 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.

Answer 1

a. Monthly deposit P = ₹250

Time period = 3 years = 3 ×12 = 36 months

Maturity value (MV) = ₹10,110

Using the RD maturity value formula:

MV = P × n + `(P xx n(n + 1) xx r)/(2 xx 12 xx 100)`

Substituting the values:

10110 = 250 × 36 + `(250 xx 36 xx 37 xx r)/(2 xx 12 xx 100)`

10110 = 9000 + `9000 xx 37r/2400`

Solving the equation gives: 

r = `4440/555` = 8%

Hence, the rate of interest is 8%.

b. If Mrs. Rao deposits ₹50 more per month, the new monthly deposit becomes:

₹250 + ₹50 = ₹300

Interest on the new deposit is calculated using:

I = `(P xx n(n + 1) xx r)/(2 xx 12 xx 100)`

Substituting the values:

I = `(300 xx 36 xx 37 xx 8)/(24 xx 100)`

I = ₹1332

Earlier interest received = ₹1110

Therefore, additional interest received:

₹1332 − ₹1110 = ₹222

So, Mrs. Rao would receive ₹222 more as interest.