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Question
The compound interest, calculated yearly, on a certain sum of money for the second year is Rs. 1320 and for the third year is Rs. 1452. Calculate the rate of interest and the original sum of money.
Solution
Compound Interest for second year = ₹ 1320
Compound Interest for third year = ₹ 1452
r = ?, P = ?
For third year: P = ₹ 1320,
I = 1452 - 1320 = ₹ 132
T = 1 year
∴ I = `("P" xx "R" xx "T")/(100)`
132 = `(1320 xx "R" xx 1)/(100)`
R = `(132 xx 100)/(1320)`
R = 10% p.a.
Now, let the principal for first year be x.
Then I = `("P" xx "R" xx "T")/(100) = (10x)/(100) = x/(100)`
Amount for first year = x + `x/(100) = (11x)/(100)`
For second year:
P = `(11 x)/(10)`, R = 10% p.a., T = 1 year
I = `((11x)/(10) xx 10 xx 1)/(100) = (11x)/(100)`
From question,
`(11x)/(100)` = 1320
⇒ x = `(1320 xx 100)/(11)`
= 12000
Thus the original sum of money is ₹12,000.
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