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Question
A man gets a simple interest of Rs. 2,000 on a certain principal at the rate of 5% p.a. in 4 years. What compound interest will the man get on twice the principal in 2 years at the same rate?
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Solution
Let the Principal amount = P
Simple Interest I = ₹ 2000
Rate of interest R = 5% p.a.
Time duration = T = 4 years
I = `"PRT"/100`
∴ 2000 = `("P" xx 5 xx 4)/100`
∴ P = 10000
Twice the principal was invested for compound interest with the same rate of interest for 2 years.
Here, P = 2 × 10,000
= ₹ 20,000
∴ Amount received,
A = P`(1 + "R"/100)^"T"`
∴ A = `20000(1 + 5/100)^2`
= `20000 xx 21/20 xx 21/20`
= 50 × 441 = 22050
I = A – P = 22050 – 20000 = 2050
The man will receive ₹ 2050 as compound interest.
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