Problem

Given below is the principal owed on a student loan last month, the annual interest rate, and the way the minimum monthly payment is computed. Find this month's minimum payment due. \begin{tabular}{|c|c|c|} \hline Principal & Annual Rate & $\begin{array}{c}\text { Method for Calculating Minimum Monthly } \\ \text { Payment }\end{array}$ \\ \hline$\$ 21,700$ & $15 \%$ & finance charge $+\$ 30+3.5 \%$ of principal \\ \hline \end{tabular} This month's minimum payment is $\$ \square$. (Round to the nearest cent as needed.)

Solution

Step 1 :Given the principal of the student loan last month was \$21700, the annual interest rate was 15\%, and the method for calculating the minimum monthly payment was the finance charge plus \$30 plus 3.5\% of the principal.

Step 2 :The finance charge is calculated by multiplying the principal by the annual interest rate and then dividing by 12 to get the monthly interest. So, the finance charge is \(\frac{21700 \times 0.15}{12} = \$271.25\).

Step 3 :The minimum monthly payment is calculated by adding the finance charge, a flat fee of \$30, and 3.5\% of the principal. So, the minimum payment is \(271.25 + 30 + 0.035 \times 21700 = \$1060.75\).

Step 4 :Final Answer: This month's minimum payment is \(\boxed{\$1060.75}\).

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Source: https://solvelyapp.com/problems/17332/

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