Final answer:
To calculate the amount Maxine must pay at the time the 16th payment is due, we need to determine the future value of the missed payments and subtract it from the total amount owed. The future value of the missed payments is $30,826.67 and the present value is $13,962.30. So, Maxine must pay $16,037.70 at the time the 16th payment is due.
Step-by-step explanation:
To calculate the amount Maxine must pay at the time the 16th payment is due, we need to first determine the future value of the missed payments.
Step 1: Calculate the future value of $800 payments for 8 years at an interest rate of 12% compounded quarterly.
Use the formula:
FV = P * [(1 + r/n)^(nt) - 1] / (r/n)
Where:
FV = Future Value
P = Payment per period (in this case $800)
r = Annual interest rate (in this case 12% or 0.12)
n = Number of compounding periods per year (in this case 4 because interest is compounded quarterly)
t = Number of years (in this case 8)
Calculate:
FV = 800 * [(1 + 0.12/4)^(4*8) - 1] / (0.12/4)
FV = 800 * (1.03^32 - 1) / 0.03
FV = 800 * (2.208 - 1) / 0.03
FV = 800 * 1.208 / 0.03
FV = 30826.67
Step 2: Calculate the present value of $800 payments for 15 periods at an interest rate of 12% compounded quarterly.
Use the formula:
PV = FV / (1 + r/n)^(nt)
Where:
PV = Present Value
FV = Future Value (in this case $30826.67)
r = Annual interest rate (in this case 12% or 0.12)
n = Number of compounding periods per year (in this case 4 because interest is compounded quarterly)
t = Number of years (in this case 15)
Calculate:
PV = 30826.67 / (1 + 0.12/4)^(4*15)
PV = 30826.67 / (1.03^60)
PV = 30826.67 / 2.208
PV = 13962.30
Step 3: Calculate the amount Maxine must pay at the time the 16th payment is due.
Subtract the present value of the missed payments from the down payment and remaining payments.
Amount = $18000 + $800*15 - $13962.30
Amount = $18000 + $12000 - $13962.30
Amount = $16037.70
Therefore, Maxine must pay $16037.70 at the time the 16th payment is due to discharge his indebtedness completely.