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Question
Find the amount and the compound interest payable annually on the following :
Rs.24000 for 1`(1)/(2)` years at 7`(1)/(2)`% per annum.
[Hint : 1 year 146 days = `1(146)/(365)"year" = 1(2)/(5)"year"`]
Solution
Rs.24000 for 1`(1)/(2)`years at 7`(1)/(2)`% per annum.
Here P = Rs.24000 , t = 1`(1)/(2)` years, r = 7`(1)/(2)`% = `(15)/(2)`%
Now, Amount after 1 year
= `"P"(1 + "r"/100)`
= `24000(1 + 15/(2 xx100))`
= `24000(1 + 3/40)`
= `24000(43/40)`
= 25800
Thus, principle for the next 6 months = Rs.25800
Interest for the next 6 months
= `(25800 xx 15 xx 6)/(200 xx 12)`
= 967.50
Therefore, amount after 1`(1)/(2)`years
= Rs.25800 + Rs.967.50
= Rs.26767.50
And CI
= A - P
= Rs.26767.50 - Rs.24000
= Rs.2767.50.
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