(a) What is the monthly payment required by the loan? (Round your answer to the nearest cent.) $ How much extra did she pay per month? (Round your answer to the nearest cent.) $ (b) How many $563 payments will she make to pay off the loan? (Round your answer up to the next whole number.) payments (c) How much does she pay in total over the life of the loan by paying $563 per month rather than the required payment? 24

(a) What is the monthly payment required by the loan? (Round your answer to the nearest cent.) $ How much extra did she pay per month? (Round your answer to the nearest cent.) $ (b) How many $563 payments will she make to pay off the loan? (Round your answer up to the next whole number.) payments (c) How much does she pay in total over the life of the loan by paying $563 per month rather than the required payment? 24

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

A recent college graduate buys a new car by borrowing $18,000 at 6%, compounded monthly, for 3 years. She decides to pay $563 instead of the monthly payment required by the loan.

**Title: Analyzing Loan Repayment Options for a New Car**

**Scenario:**
A recent college graduate buys a new car by borrowing $18,000 at an interest rate of 6%, compounded monthly, for a term of 3 years. She chooses to pay $563 per month instead of the required monthly payment.

---

**Questions:**

**(a)** What is the monthly payment required by the loan? (Round your answer to the nearest cent.)
$ _______

How much extra did she pay per month? (Round your answer to the nearest cent.)
$ _______

**(b)** How many $563 payments will she make to pay off the loan? (Round your answer up to the next whole number.)
_______ payments

**(c)** How much does she pay in total over the life of the loan by paying $563 per month rather than the required payment?
$ _______

If instead of paying $563 per month she only paid the required payment every month, how much would she have paid in total over the life of the loan? (Round your answer to the nearest cent.)
$ _______

How much will she save by paying $563 per month rather than the required payment? (Round your answer to the nearest cent.)
$ _______

---

**Discussion:**

This exercise helps in understanding the impact of paying more than the required monthly payment on a loan. By examining:

- The difference in the number of payments.
- The total amount paid over the loan’s lifespan.
- Potential savings achieved by paying extra each month.

This analysis can guide individuals in making informed financial decisions regarding loan repayments.

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