What monthly payment, beginning next month, is required over the next 48 months to pay off a $10,000 debt today, if interest is charged at 10% per year, compounded monthly?
Click on the arrows to vote for the correct answer
A. B. C. D. E.A
On the BAII Plus, press 48 N, 10 divide 12 = I/Y, 10000 PV, 0 FV, CPT PMT. On the HP12C, press 48 n, 10 ENTER 12 divide i, 10000 PV, 0 FV, PMT. Make sure the BAII Plus has the P/Y value set to 1.
To calculate the monthly payment required to pay off a debt, we can use the formula for the monthly payment on an amortizing loan. The formula is given by:
P=1−(1+r)−nr⋅PV
Where: P = Monthly payment r = Monthly interest rate PV = Present value of the debt (initial loan amount) n = Number of periods (number of months)
In this case, the present value of the debt is $10,000, the annual interest rate is 10%, and interest is compounded monthly. Therefore, we need to convert the annual interest rate to a monthly rate.
The monthly interest rate (r) can be calculated by dividing the annual interest rate by 12 (number of months in a year):
r=1210%=0.10÷12=0.00833 (rounded to 5 decimal places)
The number of periods (n) is given as 48 months.
Now we can substitute the values into the formula and solve for P:
P=1−(1+0.00833)−480.00833⋅10,000
Calculating the denominator first:
1+0.00833=1.00833
(1+0.00833)−48=1.00833−48
Using a calculator:
(1+0.00833)−48≈0.59821 (rounded to 5 decimal places)
Now we can substitute the values into the formula:
P=1−0.598210.00833⋅10,000
P=0.4017983.30
P≈207.28 (rounded to 2 decimal places)
Therefore, the monthly payment required over the next 48 months to pay off a $10,000 debt at an interest rate of 10% per year, compounded monthly, is approximately $207.28.
None of the provided answer choices match exactly with this result. However, the closest option is C. $216.02.