Question

A loan of $12,651 was repaid at the end of 8 months What size repayment check (principal and interest) was written, if a 7.5% annual rate of interest was charged?The amount of the repayment check was $(Round to two decimal places)

Answer 1

We have a loan with a principal of $12,651.

It is paid in 8 monthly payments.

The annual rate of interest is 7.5%.

We then have to calculate the amount of each monthly payment.

This can be calculated using the annuity formula with subperiods.

The formula is:

$M=\frac{P\cdot\frac{r}{m}}{1-(1+\frac{r}{m})^{n\cdot m}}$

For this problem we have a principal P = 12,651, an interest rate r = 0.075, the subperiods are months so m = 12, and the number of payments is n*m = 8.

We can replace and solve as:

$\begin{gathered} M=\frac{12651\cdot\frac{0.075}{12}}{1-(1+\frac{0.075}{12})^{-8}} \\ M=\frac{12651\cdot0.00625}{1-(1+0.00625)^{-8}} \\ M=\frac{79.06875}{1-(1.00625)^{-8}} \\ M\approx\frac{79.06875}{1-0.95138} \\ M\approx\frac{79.06875}{0.04862} \\ M\approx1626.26 \end{gathered}$

Answer: the monthly payment in each check was $1626.26.