Question

Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced. Assume that you take out a $3000 loan for 30 months at 9% APR. How much of the first month's payment is interest? (Round your answer to the nearest cent.)

Answer 1

Given parameters:

`\begin{gathered} P=Loan\text{ amount=\$3000} \\ r=rate\text{ intersest per period=9\%=}(9)/(100*12)=(0.09)/(12)=0.0075 \\ n=n\\u mber\text{ of payments=30 months} \\ \end{gathered}`

We can now apply the formula below to calculate the payment amount per period

`A=P(r(1+r)^n)/((1+r)^n-1)`

`\begin{gathered} A=3000*(0.0075(1+0.0075)^(30))/((1+0.0075)^(30)-1) \\ \\ A=3000*(0.0075(1.25127))/((1.25127)-1)=(28.1536)/(0.25127)=112.05 \end{gathered}`

Thus his monthly payment will be $112.05

But since we have to get the interest on the first month's pay,

The interest is

`r* P=0.0075*3000=\text{ \$22.5}`

Thus, $22.50 is the interest on the first month's payment