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Question
The compound interest payable annually on a certain sum for 2 years is Rs 40.80 and the simple interest is Rs 40. Find the sum and the rate percent.
Solution
Let sum be Rs. P and r % be the rate of interest.
We have t = 2 years, C.I. = Rs.40.80 and S.I. = Rs.40
Since, Simple interest
= `("P" xx "r" xx "t")/(100)`
⇒ 40 = `("P" xx "r" xx 2)/(100)`
⇒ Pr = `(4000)/(2)`
= 2000
Now,
C.I. = A - P
= `"P"(1 + "r"/100)^"t" - "P"`
= `"P"[(1 + "r"/100)]^"t" - 1]`
⇒ 40.80 = `"P"[(1 + "r"/100)^2 - 1]`
⇒ 40.80 = `"P"(1 + "r"^2/10000 + (2"r")/100 - 1)`
⇒ 40.80 = `"P"("r"^2/10000 + (2"r")/100)`
⇒ 40.80 = `"Pr"("r"/10000 + (2)/100)`
⇒ 40.80 = `2000(("r" + 200)/10000)`
⇒ 40.80 = `("r" + 200)/(5)`
⇒ r = 40.80 x 5 - 200
= 204 - 200
= 4
Hence, r = 4%
Now, Pr = 2000
⇒ P = `(2000)/"r"`
= `(2000)/(4)`
= 500.
Thus, sum is Rs.500 and rate of interest is 4%.
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