Math Problem Statement

Compute the monthly payment and the total amount spent for a vehicle that costs ​$16 comma 100 if you finance the entire purchase over 5 years at an annual rate of 8.75 percent. Calculate the payment if you finance the car for only four years.​ Finally, calculate the payment for three years. What do you notice about the payment under the different time​ assumptions? ​Note: Round intermediate computations to at least five​ (5) decimal places. Click on the table icon to view the MILPF table LOADING.... Question content area bottom Part 1 The monthly​ payment, PMT​, on the​ 5-year auto loan is ​$

enter your response here.  ​(Round to the nearest​ cent.) Part 2 The total amount spent if you financed ​$16 comma 100 for 5 years at 8.75 percent per year is ​$

enter your response here. ​(Round to the nearest​ cent.) Part 3 The monthly​ payment, PMT​, on the​ 4-year auto loan is ​$

enter your response here.  ​(Round to the nearest​ cent.) Part 4 ​Finally, the monthly​ payment, PMT​, on the​ 3-year auto loan is ​$

enter your response here.  ​(Round to the nearest​ cent.) Part 5 What do you notice about the payment under the different time​ assumptions?  ​(Select the best choice​ below.) A. As the number of payments​ decreases, the monthly payment​ decreases, all else equal. The shorter the borrowing​ period, the lower the monthly payments. B. As the number of payments​ decreases, the monthly payment​ increases, all else equal. The shorter the borrowing​ period, the higher the monthly payments.

Solution

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Math Problem Analysis

Mathematical Concepts

Loan Amortization
Compound Interest
Monthly Payments
Time Value of Money

Formulas

PMT = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Total Amount Spent = PMT * n

Theorems

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Suitable Grade Level

Grades 9-12