Question

David opened a Recurring Deposit Account in a bank and deposited Rs. 300 per month for two years. If he received Rs. 7,725 at the time of maturity, find the rate of interest per annum.

Answer 1

Instalment per month (P) = Rs. 300

Number of months (n) = 24

Let rate of interest (r) = r% p.a

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

= `300 xx (24(24 + 1))/(2 xx 12) xx r/100`

= `300 xx 600/24 xx r/100`

= Rs. (75)r

Maturity value = Rs. (300 × 24) + Rs. (75)r

Given maturity value = Rs. 7,725

Then Rs. (300 × 24) + Rs. (75)r = Rs. 7,725

⇒ 75r = Rs. 7,725 – Rs. 7,200

⇒ r = `525/75`

= 7%

Answer 2

Deposit during one month (P) = Rs. 300

Period = 2 years = 24 months.

Maturity value = Rs. 7725

Let R be the rate percent, then

Now principal for 1 month

= `(P xx n(n + 1))/(2)`

= `(300 xx 24(24 + 1))/(2)`

= `(300 xx 24 xx 25)/(2)`

= Rs. 90000

∴ Interest earned

= `"PRT"/100`

= `(90000 xx R xx 1)/(100 xx 12)`

= 75R

Now 300 × 24 + 75R = 7725

⇒ 7200 + 75R = 7725

⇒ 75R

= 7725 – 7200

= 525

⇒ R = `(525)/(75)` = 7

∴ Rate of Interest = 7% p.a.