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)
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