Question

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​

Answer 1

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.