Math Problem Statement

Suppose you take out a

3535​-year

​$250 comma 000250,000

mortgage with an APR of

66​%.

You make payments for

33

years

​(3636

monthly​ payments) and then consider refinancing the original loan. The new loan would have a term of

2020

​years, have an APR of

5.15.1​%,

and be in the amount of the unpaid balance on the original loan.​ (The amount you borrow on the new loan would be used to pay off the balance on the original​ loan.) The administrative cost of taking out the second loan would be

​$23002300.

Use the information to complete parts ​(a) through​ (e) below.

Question content area bottom

Part 1

a. What are the monthly payments on the original​ loan?

​$enter your response here

​(Round to the nearest cent as​ needed.)

Part 2

b. A short calculation shows that the unpaid balance on the original loan after

33

years is

​$243 comma 097.53243,097.53​,

which would become the amount of the second loan. What would the monthly payments be on the second​ loan?

​$enter your response here

​(Round to the nearest cent as​ needed.)

Part 3

c. What would be the total amount you would pay if you continued with the original

3535​-year

loan without​ refinancing?

​$enter your response here

​(Round to the nearest cent as​ needed.)

Part 4

d. What would be the total amount you would pay with the​ refinancing?

​$enter your response here

​(Round to the nearest cent as​ needed.)

Part 5

e. Compare the two options and decide which one you would choose. What other factors should be considered in making the​ decision?

The best option would be to

▼   continue paying the original loan,

refinance the loan,

assuming that you can afford the monthly payments.

Solution

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Math Problem Analysis

Mathematical Concepts

Mortgage Payments
Interest Rates
Loan Refinancing
Time Value of Money

Formulas

M = P × (r(1 + r)^n) / ((1 + r)^n - 1)
Total Amount Paid = M × n

Theorems

Compound Interest Formula
Loan Amortization Formula

Suitable Grade Level

College-Level (Finance/Math)