Question

A debt of $5000 due four years from now and $5000 due nine years from now is to be repaid by a payment of $2000 in one year, a payment of $4000 in three years, and a final payment at the end of five years. If the interest rate is 1.8% compounded annually, how much is the final payment?

Answer 1

To find the final payment, calculate the present value of the future debts and subtract the total of the past payments. The final payment at the end of five years is $2408.69.

Step-by-step explanation:

To find the final payment, we need to calculate the present value of the two future debts and subtract the total of the two payments made in the past. We can use the formula for present value of a future amount:

Present Value = Future Value / (1 + Interest Rate)n

For the first debt of $5000 due four years from now, the present value is:

$5000 / (1 + 0.018)4 = $4623.73

For the second debt of $5000 due nine years from now, the present value is:

$5000 / (1 + 0.018)9 = $3784.96

So, the total present value of the debts is $4623.73 + $3784.96 = $8408.69. Subtracting the past payments, we get:

$8408.69 - $2000 - $4000 = $2408.69.

Therefore, the final payment at the end of five years is $2408.69.