Questions: The owner of a construction company purchased a cement mixer truck for 180,000 and made a down payment of 45,000. The remaining balance was financed for 10 years at an annual interest rate of 7.25% compounded monthly. Find the monthly payment (in dollars). (Round your answer to the nearest cent.)

The owner of a construction company purchased a cement mixer truck for 180,000 and made a down payment of 45,000. The remaining balance was financed for 10 years at an annual interest rate of 7.25% compounded monthly. Find the monthly payment (in dollars). (Round your answer to the nearest cent.)

Transcript text: The owner of a construction company purchased a cement mixer truck for $\$ 180,000$ and made a down payment of $\$ 45,000$. The remaining balance was financed for 10 years at an annual interest rate of $7.25 \%$ compounded monthly. Find the monthly payment (in dollars). (Round your answer to the nearest cent.) \$ $\square$ Need Help? Read It $\square$ Master it

Solution

Solution Steps

Step 1: Calculate the Loan Amount (L)

To find the amount financed, subtract the down payment from the total purchase price: $L = P - D = 180000 - 45000 = 135000$.

Step 2: Convert the Annual Interest Rate to a Monthly Rate (r)

The monthly interest rate is obtained by dividing the annual interest rate by the number of compounding periods per year: $r = \frac{R}{12} = \frac{7.25}{12} = 0.604$.

Step 3: Convert the Loan Term in Years to Months (n)

The total number of payments is calculated by multiplying the loan term in years by the compounding frequency: $n = T \times 12 = 10 \times 12 = 120$.

Step 4: Calculate the Monthly Payment (M)

Using the formula for the monthly payment of a loan with compound interest: $M = \frac{L \times \frac{r}{100}}{1 - (1 + \frac{r}{100})^{-n}} = \frac{135000 \times \frac{0.604}{100}}{1 - (1 + \frac{0.604}{100})^{-120}} = 1584.91$.