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Question
A certain sum of money is put at compound interest, compounded half-yearly. If the interest for two successive half-years are Rs. 650 and Rs. 760.50; find the rate of interest.
Solution 1
∵ Difference between the C.I. of two successive half-years
= Rs. 760.50 - Rs. 650= Rs. 110.50
⇒ Rs. 110.50 is the interest of one half-year on Rs. 650
∴ Rate of interest = Rs. `[100 xx 1]/[ P xx T ] %`
= `(100 xx 110.50)/(650 xx 1/2)%`
= 34%
Solution 2
Let sum of money = P, Rate = r % half-yearly.
Simple interest for I half-year on sum = Rs. 650.
Simple interest for II half-year on sum = P + 650 = Rs. 760.50
∵ Difference between the C.I. of two successive half-years
= Rs. 760.50 - Rs. 650= Rs. 110.50
⇒ Rs. 110.50 is the interest of one half-year on Rs. 650.
Simple interest (S.I.) = `(P xx R xx T)/100`
∴ `110.50 = (650 xx R xx 1)/100`
∴ 110.50 = 6.5 × R
∴ `(110.50)/(6.5)` = R
∴ R = 17% Per half-yearly
∴ Rate of interest = 17 × 2 = 34% p.a.
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