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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.
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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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