What monthly payment, beginning next month, is required over the next 60 months to pay off a $10,000 debt today, if interest is charged at 14% per year, compounded monthly?
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A. B. C. D. E.E
On the BAII Plus, press 60 N, 14 divide 12 = I/Y, 10000 PV, 0 FV, CPT PMT. On the HP12C, press 60 n, 14 ENTER 12 divide i, 10000 PV, 0 FV, PMT. Make sure the BAII Plus has the P/Y value set to 1.
To determine the monthly payment required to pay off a $10,000 debt over 60 months at an annual interest rate of 14% compounded monthly, we can use the formula for the monthly payment on an amortizing loan. The formula is given as:
P = (r * PV) / (1 - (1 + r)^(-n))
Where: P = Monthly payment PV = Present value (initial debt) r = Monthly interest rate n = Number of periods (months)
In this case, the present value (PV) is $10,000, the annual interest rate is 14%, and the number of periods (n) is 60 months. To calculate the monthly interest rate (r), we divide the annual interest rate by 12 (number of months in a year).
r = 0.14 / 12 r = 0.0117 (rounded to four decimal places)
Substituting these values into the formula:
P = (0.0117 * 10,000) / (1 - (1 + 0.0117)^(-60))
Now we can solve for P:
P = (0.0117 * 10,000) / (1 - (1 + 0.0117)^(-60)) P = 116.02 (rounded to two decimal places)
Therefore, the monthly payment required, beginning next month, to pay off the $10,000 debt over the next 60 months at an annual interest rate of 14% compounded monthly, is $116.02.
So the correct answer is option A: $116.02.