Question

Mr. Ahuja deposited ₹ 500 per month in an R.D. account for a period of 3 years. He received ₹ 20,220 at the time of maturity. Find:

1. rate of interest.
2. how much more interest Mr. Ahuja will receive, if he had deposited ₹ 100 more every month.

Answer 1

Given,

n = 3 years = 36 months, P = ₹ 500

Let r be the rate of interest.

Maturity amount = ₹ 20,220

Total amount deposited = 500 × 36 = ₹ 18,000.

Interest received = Maturity amount − Amount deposited

= ₹ 20,220 − ₹ 18,000

= ₹ 2,220.

(i) By formula,

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

Substituting values we get:

⇒ 2,220 = `500 xx (36 xx (37))/24 xx r/100`

⇒ 2,220 = `500 xx 1332/24 xx r/100`

⇒ 2,220 = `500 xx 55.5 xx r/100`

⇒ 2,220 = `27750 xx r/100`

⇒ 2,220 = 277.5r

r = `(2,220)/277.5`

r = 8

Hence, rate of interest = 8% p.a.

(ii) If Mr. Ahuja had deposited ₹ 100 more per month then the monthly deposit would have been ₹ 600.

By formula,

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

Substituting values we get:

⇒ I = `600 xx (36 xx (37))/24 xx 8/100`

⇒ I = `600 xx 55.5 xx 8/100`

⇒ I = 600 × 4.44

⇒ I = ₹ 2,664

The difference in the interest Mr. Ahuja received.

= ₹ 2,664 − ₹ 2,220

= ₹ 444

Hence, Mr. Ahuja would receive ₹ 444 more interest if he deposited ₹ 100 more per month.