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Question

Sanju puts equal amount of money, one at 10% per annum compound interest payable half-yearly and the second at a certain rate per annum compound interest payable yearly. If he gets equal amounts after 3 years what is the value of the second rate percent?

A
1014%
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B
10%
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C
912%
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D
814%
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Solution

The correct option is C 1014%
Given that, Sanju puts the same amount of money, one at 10% per annum compound interest, compounded half-yearly, and other at some interest per annum compound interest, compounded annually.
He receives the same amount after 3 years.
To find out: The rate of interest for the second investment.

Let the principal amount be Rs. x. And the amount received after 3 years be A
Also, let the rate of interest in the second case be y% per annum.

In the first case, the payment is made half-yearly at 10%.
So the number of time in 3 years=3÷12=6 and
the rate =10%÷2=5%

In CI, we know that the amount (A)=P(1+R100)T
Here, P=x, R=5% and T=6
A=x(1+5100)6.

Now, in the second case, P=x, R=y% and T=3
A=x(1+y100)3.

Given that, the amount received in both cases is the same.
Hence, x(1+y100)3=x(1+5100)6

(1+y100)3={(1+5100)2}3

(1+y100)=(1+5100)2=441400

y100=4414001

y100=41400

y=414=1014%

Hence, the required rate of interest for the second case is 1014%.

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