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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.
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Solution
Given:
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)`
I = `(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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