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.

Answer 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%

Answer 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.