Problem

Angela's bank gave her a 3-year add-on interest loan for $\$ 7,680$ to pay for new equipment for her antiques restoration business. The annual interest rate is $11.98 \%$. How much interest will she pay? What are her monthly payments? She will pay $\$ 2760.19$ in interest on the loan. (Round to the nearest cent.) Her monthly payments are $\$ \square$. (Round to the nearest cent.)

Solution

Step 1 :First, we need to calculate the total interest Angela will pay over the 3-year period. The formula for calculating the total interest on an add-on interest loan is: \(\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}\)

Step 2 :Where: \(\text{Principal} = \$7680\), \(\text{Rate} = 11.98\% = 0.1198\) in decimal form, and \(\text{Time} = 3\) years.

Step 3 :Using these values, we find that the total interest Angela will pay is \(\text{Interest} = \$7680 \times 0.1198 \times 3 = \$2760.19\)

Step 4 :Next, we calculate the total amount Angela needs to repay, which is the sum of the principal and the interest. So, \(\text{Total Repayment} = \text{Principal} + \text{Interest} = \$7680 + \$2760.19 = \$10440.19\)

Step 5 :Finally, we calculate her monthly payments by dividing the total repayment amount by the total number of months in the loan period (3 years = 36 months). So, \(\text{Monthly Payments} = \frac{\text{Total Repayment}}{\text{Number of Months}} = \frac{\$10440.19}{36} = \$290.01\)

Step 6 :Final Answer: Angela will pay \(\boxed{\$2760.19}\) in interest on the loan. Her monthly payments are \(\boxed{\$290.01}\)

From Solvely APP
Source: https://solvelyapp.com/problems/38434/

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