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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.
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Solution 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%
Solution 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.
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