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Question
Find the compound interest for `2 1/2` years on ₹ 4000 at 10% p.a, if the interest is compounded yearly
Solution
Principal (P) = ₹ 4000
r = 10% p.a
Compounded yearly
n = `2 1/2` years.
Since it is of the form `"a" "b"/"c"` years
Amount (A) = `(1 + "r"/100)^"n" (1 + ("b"/"c" xx "r")/100)`
= `4000(1 + 10/100)^2 (1 + (1/2 xx 10)/100)^1`
= `4000 xx (110/100)^2 xx (105/100)^1`
= 4000 × 1.1 × 1.1 × 1.05
= 5082
∴ C.I. = Amount – Principal
= 5082 – 4000
= 1082
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