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Question
The simple interest on an amount for 2 years at 8% is Rs 320. Calculate the compound interest on the same amount at the same rate for 1 year if the interest is compounded half-yearly.
Solution
Here, P = ? ; t = 2 years ; r = 8 % p.a.
S.I. = Rs 320
P = Rs `("S.I." xx 100)/("r" xx "t")`
P = Rs `(320 xx 100)/(8 xx 2)`
P = Rs 2,000
Now, P =Rs 2,000 ; t = 1 year
n = 2t = 2 × 1=2
r = `1/2 xx 8 % = 4 %` Per conversion period.
`"A" = "P" (1 + "r"/100)^"n"`
A = Rs 2000 `(1 + 4/100)^2`
= Rs 2,000 x1.04 x 1.04 = Rs 2,163.20
C.I. =A - P
= Rs (2, 163.20 - 2,000)
=Rs 163.20
Hence, compound interest= Rs 163.20
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