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Question
Arif took a loan of Rs 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after `1 1/2` years if the interest is
(1) Compounded annually
(2) Compounded half yearly
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Solution
1) P = Rs 80,000
R = 10% per annum
n = `1 1/2` years
The amount for 1 year and 6 months can be calculated by first calculating the amount for 1 year using the compound interest formula, and then calculating the simple interest for 6 months on the amount obtained at the end of 1 year.
Firstly, the amount for 1 year has to be calculated.
A = Rs `[80000 (1 + 10/100)^1]`
= Rs `[80000 (1 + 1/10)] = Rs (80000 xx 11/10) = Rs 88000`
By taking Rs 88,000 as principal, the SI for the next `1/2` year will be calculated.
S.I = `"P x R x T"/100` = Rs `((88000xx10xx1/2)/100)` = Rs 4400
Interest for the first year = Rs 88000 − Rs 80000 = Rs 8,000
And interest for the next `1/2` year = Rs 4,400
Total C.I. = Rs 8000 + Rs 4,400 = Rs 1,2400
A = P + C.I. = Rs (80000 + 12400) = Rs 92,400
2) The interest is compounded half yearly.
Rate = 10% per annum = 5% per half year
There will be three half years in `1 1/2` years.
A = Rs`[80000 (1 + 5/100)^3] = Rs [80000(1 + 1/20)^3]`
= Rs`(80000 xx 21/20 xx 21/20 xx 21/20)` = Rs 92610
Difference between the amounts = Rs 92,610 − Rs 92,400 = Rs 210
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