Question

# For the following loans, make a table showing the amounts of each monthly payment that go toward principal and interest for the first 3 months of the loan. A student loan of $\ 24,000$ at a fixed APR of $8 \%$ for $15$ years

Solution

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The goal is to construct a table representing the first three months of the loan, indicating the amounts of each monthly payment toward principal and interest, given that the amount borrowed is $\24000$ with an annual percentage rate of $8\%$ for $15$ years.

To construct the table, find the monthly interest rate, the monthly payment, the interest payment due at the end of the first, second, and third months, and the new loan principal.

To determine the monthly payment, apply Loan Payment Formula:

$PMT=\dfrac{P\times \frac{APR}{n}}{[1-(1+\frac{APR}{n})^{-nY}]}$

where $PMT$ is the monthly payment, $P$ is the starting loan principal, $APR$ is the annual percentage rate (as a decimal), $n$ is the number of payment periods per year, and $Y$ is the loan term in years.