Question

Premlata deposits ₹ 5,000 in an R.D. account at 8% p.a. rate of interest. How much per month must she deposit to get the same interest when the rate of interest is increased by 2%. Time in both the cases is same.

Answer 1

Let the time in both the cases be n months.

In first case:

P = ₹ 5,000, r = 8%

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

`I_1 = 5,000 xx (n(n + 1))/24 xx 8/100`

In second case:

New rate of interest (r) = 8% + 2%

= 10%

Let new monthly deposit = x

`I_2 = x xx (n(n + 1))/24 xx 10/100`

Since interest is same,

⇒ `5,000 xx (n(n + 1))/24 xx 8/100 = x xx (n(n + 1))/24 xx 10/100`

⇒ `5,000 xx 8/100 = x xx 10/100`

⇒ 5000 × 8 = 10x

⇒ 40000 = 10x

⇒ x = 4000.

Hence, Premlata must deposit ₹ 4,000 per month to get the same interest when the rate of interest is increased by 2%.