Question

A debt of $1000 with interest j₄= 10% will be repaid by a payment of $200 at the end of 3 months and three equal payments at the end of 6, 9 and 12 months. What will these payments be?

a. $200

b. $304.34

c. $358.89

d. $288.86

Calculated several times, the number I got was 338.355 which is not one of the answers

Answer 1

Solution:-

Let the equalised payments be x.

We know that the interest rate charged on the debt is 10%. So, the present value of all payments made discounted at 10% would have a present value of $1,000. Based on this, following is the equation:

1,000= 200*(1/102.5%) + x*(1/105%) + x*(1/107.5%) + x*(1/110%)

1,000= 194+ x*(0.95+0.93+0.91)

x*2.79 = 806

x= $288.8

Therefore, the three equal payments are $288.8 and the correct option is d.