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Question
The difference between simple interest and compound interest on a certain sum of money is Rs. 32 at 8% per annum for 2 years. Find the amount.
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Solution
Compound Interest = A – P
= `"P"(1 + "R"/100)^"T" - "P"`
Simple interest = `"PRT"/100`
Given R = 8%, T = 2 years and
compound interest – simple interest = ₹ 32
∴ `"P"[(1 + "R"/100)^"T" - 1] - "PRT"/100 = 32`
i.e. `"P"([(1 + 8/100)^2 - 1] - (8 xx 2)/100) = 32`
`"P" = ([(108/100)^2 - 1] - 8/50)` = 32
P[(1.08)2 − 1 − 0.16] = 32
P[1.1664 − 1.16] = 32
∴ 0.0064 P = 32
P = `32/0.0064`
= `320000/64`
= `10000/2`
p = ₹ 5000
∴ The man will receive a compound interest of ₹ 5000
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