Question

A sum of Rs 6,000 was taken as a loan. This is to be repaid in two equal annual installments. If the rate of interest is 20% compounded annually then find the value of each installment.

A. Rs. 3000
B. Rs. 4320
C. Rs. 6000
D. Cannot be determined

Answer 1

The value of each installment is approximately Rs. 3923.87.

How to find the value of each installment

To find the value of each installment, use the formula for the present value of an annuity.

The formula for the present value of an annuity is:

`PV = PMT * [1 - (1 + r)^(-n)] / r`

Where:

PV is the present value (loan amount)

PMT is the payment per period (installment amount)

r is the interest rate per period (annual interest rate divided by the number of compounding periods)

n is the total number of periods (in this case, the number of installments)

Given:

Loan amount (PV) = Rs 6,000

Number of installments (n) = 2

Annual interest rate (r) = 20%

First, lt's calculate the interest rate per period:

r = 20% / 1 = 20%

Next, we can substitute the values into the formula and solve for PMT:

`PV = PMT * [1 - (1 + r)^(-n)] / r`

Rs 6,000 = PMT *
`[1 - (1 + 20%)^(-2)]`/ 20%

Simplifying the equation:

`PMT * [1 - (1 + 0.20)^(-2)] / 0.20 = Rs 6,000\\PMT * [1 - (1.20)^(-2)] / 0.20 = Rs 6,000`

PMT * [1 - 0.6944] / 0.20 = Rs 6,000

PMT * 0.3056 / 0.20 = Rs 6,000

PMT * 1.528 = Rs 6,000

PMT = Rs 6,000 / 1.528

PMT ≈ Rs 3923.87

Therefore, the value of each installment is approximately Rs. 3923.87.