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Question
Simple interest on a sum of money for 2 years at 4% is Rs 450. Find the compound interest at the same rate for 1 year if the interest is reckoned half-yearly.
Solution
Since Simple interest
= `("P" xx "r" xx "t")/(100)`
⇒ 450 = `("P" xx 4 xx 2)/(100)`
⇒ P = `(45000)/(8)`
= 5625
Now for C.I., P = Rs.5625, r = 4, t = 1 year
Here P1 = Rs.5625 and rate of interest for half-yearly = 2%
So, Amount after `(1)/(2)` year
= `"P"(1 + "r"/100)`
= `5625(1 + 2/100)`
= `5625 xx (102)/(100)`
= 5737.50
Thus, P2 = Rs.5737.50 and r = 2%
Amount after 1 year
= `"P"(1 + "r"/100)`
= `5737.50(1 + 2/100)`
= `5737.50 xx (102)/(100)`
= 5852.25
Hence, Amount = Rs.5852.25
Also, C.I.
= A - P
= Rs.5852.25 - Rs.5625
= Rs.227.25.
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