Question

Mohammad divide Rs 82000 into two parts such that the amounts at 5% per annum compound interest in 2 years and 3 years are equal respectively.How much amount does he divide?

Answer 1

Rs 42000 and Rs 40000

Explanation:

Given that Rs 82000 is divided into two parts.

Let the first part be Rs x which is compounded annually at the interest of 5% per annum for 2 years.

The rate of interest = 5%=0.05

The total amount after 2 years
`= x(1+0.05)^(2)\cdots(i)`

The other part is Rs 82000-x which is compounded annually at the interest of 5% per annum for 3 years.

The total amount after 3 years
`= (82000-x)(1+0.05)^(3)\cdots(ii)`

As both the amounts are equal, so from equation (i) and (ii)

`x(1+0.05)^(2)=(82000-x)(1+0.05)^(3) \\\\x(1.05)^(2)=82000(1.05)^(3) -x(1.05)^(3) \\\\x(1.05^2+1.05^3)=82000* 1.05^3 \\\\x(2.260125)=94925.25 \\\\x=94925.25/2.260125 \\\\`

x= 42000

And the other part = 82000-42000 = Rs 40000

Hence, he divides the money as

Rs 42000 at 5% per annum compound interest in 2 years and

Rs 40000 at 5% per annum compound interest in 3 years.