Question

Debt payments of $10,000 due 30 months ago from today, $6,000 due today and $4,000 due in 2 years from today, are to be replaced by one single equivalent value payment in 9 months from today. If the cost of money is 6% p.a. and the focal point is in 9 months from today, how large is that unknown payment? (3 marks)

a) What is the value of the $10,000 at the focal point?
b) What is the value of the $6,000 at the focal point?
c) What is the value of the $4,000 at the focal point?
d) What is the size of the large payment at the focal point (in 9 months) that replaces all three numbers?

Answer 1

The unknown payment that will replace the three debt payments is $18,384.53 at the focal point in 9 months from today.

Step-by-step explanation:

To calculate the present value of the three debt payments, we need to discount each amount back to the focal point (9 months from today) using the given interest rate of 6% p.a. Let's calculate each value:

1. The present value of the $10,000 debt payment due 30 months ago is $10,000/(1+0.06)^(30/12) = $8,872.91.
2. The present value of the $6,000 debt payment due today is $6,000/(1+0.06)^(0/12) = $6,000.
3. The present value of the $4,000 debt payment due in 2 years is $4,000/(1+0.06)^(24/12) = $3,511.62.

To find the unknown payment that will replace these three amounts, we sum up the present values and solve for the unknown payment:

$8,872.91 + $6,000 + $3,511.62 = $18,384.53

Therefore, the unknown payment that will replace the three debt payments is $18,384.53 at the focal point in 9 months from today.