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प्रश्न
The simple interest on a certain sum of money for 3 years at 5% per annum is Rs.1,200. Find the amount and the compound interest due on this sum of money at the same rate and after 2 years. Interest is reckoned annually.
उत्तर
Let Rs.X be the sum of money.
Rate = 5 % p.a. Simple interest = Rs.1,200, n = 3 years.
`1,200 = [ "X" xx 5 xx 3 ]/100`
⇒ X = `[ 12,00,000 ]/15`
⇒ X = 8,000
The amount due and the compound interest on this sum of money at the same rate and after 2 years.
P = Rs. 8,000 ; rate = 5% p.a., n = 3 years
∴ A = P`( 1 + r/100 )^n`
⇒ A = 8,000`( 1 + 5/100 )^2`
⇒ A = 8,000( 1.1025 )
⇒ A = 8,820
C.I. = A - P
⇒ C.I. = 8,820 - 8,000
⇒ C.I. = 820.
The amount due after 2 years is Rs. 8,820 and the compound interest is Rs. 820.
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