Question

A debt of $5000 due 5 years from now and $5000 due 10 years from now is to be repaid by a payment of $2000 in 2 years, a payment of $4000 in 4 years, and a final payment at the end of 6 years. If the interest rate is 2.5% compounded annually, how much is the final payment?

Answer 1

The final payment is $675.04.

Step-by-step explanation:

To find the final payment, we need to calculate the present value of the two future payments using the formula:

• Present Value = Future Value / (1 + interest rate)^n

For the $5000 due 5 years from now, the present value is:

• Present Value = $5000 / (1 + 0.025)^5 = $5000 / 1.13140625 = $4416.29 (rounded to two decimal places)

For the $5000 due 10 years from now, the present value is:

• Present Value = $5000 / (1 + 0.025)^10 = $5000 / 1.28008454 = $3906.67 (rounded to two decimal places)

To find the final payment, subtract the present values of the two future payments from the total debt:

• Final Payment = Total Debt - Present Value of $5000 (due 5 years from now) - Present Value of $5000 (due 10 years from now)
• Final Payment = $5000 - $4416.29 - $3906.67 = $675.04 (rounded to two decimal places)