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Question
Geeta borrowed Rs. 15,000 for 18 months at a certain rate of interest compounded semi-annually. If at the end of six months it amounted to Rs. 15,600; calculate :
(i) the rate of interest per annum.
(ii) the total amount of money that Geeta must pay at the end of 18 months in order to clear the account.
Solution
For 1st half - year :
P= Rs. 15,000; A= Rs. 15,600 and T = ½ year
Interest = Rs. 15,600 - Rs. 15,000= Rs. 600
Rate= `["I" xx 100 ]/["P" xx "T"] %
= [600 xx 100]/[15,000 xx 1/2]` % = 8% .
For 2nd half - year :
P = Rs. 15,600; R = 8% and T = `1/2` year
Interest = Rs. `[15,600 xx 8 xx 1/2 ]/[100]` = Rs. 624
Amount = Rs. 15,600 + Rs. 624 = Rs. 16,224
For 3rd half - year :
P = Rs. 16,224; R = 8 % and T = `1/2` year
Interest = Rs. `[16,224 xx 8 xx 1/2 ]/[100]` = Rs. 648.96
Amount = Rs. 16,224 + Rs. 648.96 = Rs. 16,872.96.
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