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Sum compounded alluny

Shar
d) The difference between the annual and semi-annual compound interest on
of money is Rs 482 at the rate of 20 % per annum for 2 years. Find the sum​

1 Answer

4 votes

Answer:

Rs 20000

Explanation:

Let the sum is x.

The rate of interest, r=20%=0.2

Time, t=2 years.

Total amount after t years,
A= x \left(1+(r)/(n)\right)^(tn)

The value of n when compounded annually, n=1

So, the total amount,


A_1=x \left(1+(0.2)/(1)\right)^(2* 1)=x(1.2)^2

The compound interest when compounded annually,


I_1 =x(1.2)^2-x

The value of n when compounded semi-annually, n=2

So, the total amount,
A_2 = x \left(1+(0.2)/(2)\right)^(2* 2)=x(1.1)^4

The compound interest when compounded semi-annually,


I_2 =x(1.1)^4-x

As the difference between the annual and semi-annual compound interest on x amount of money is Rs 482, so


I_2-I_1=482 \\\\(x(1.1)^4-x)-(x(1.2)^2-x)=482 \\\\x(1.1)^4-x(1.2)^2=482 \\\\x(1.1^4 - 1.2^2) = 482 \\\\x(0.0241) = 482 \\\\x=482/0.0241 \\\\

x=20000

Hence, the sum is Rs 20000.

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