# Math

Suppose you take out a 45​-year ​\$100,000 mortgage with an APR of 6​%. You make payments for 2 years ​(24 monthly​ payments) and then consider refinancing the original loan. The new loan would have a term of 20 ​years, have an APR of 5.9​%, 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 ​\$2500. Use the information to complete parts ​(a) through​ (d) below

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

b. A short calculation shows that the unpaid balance on the original loan after 2 years is ​\$99,077.21​, which would become the amount of the second loan. What would the monthly payments be on the second​ loan?

c. What would be the total amount you would pay if you continued with the original 45​-year loan without​ refinancing?

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

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1. for first part:
i = .06/12 = .005
n = 45(12) = 540
let the payment be p
p(1 - 1.005^-540)/.005 = 100000
I get p = \$536.2846

Now, you are doing this for 24 months
outstanding balance = 100000(1.005)^24 - 536.2846(1.005^24 - 1)/.005
= \$99,077.21 , as stated in the problem

Plus the admin fee of 2500 gives you a balance of 101577.21
MORE THAN WHAT YOU STARTED WITH 2 YEARS AGO !!!!

new i = .00491666...
new n = 20(12) = 240
new payment --- q

q(1 - 1.00491666..^-240)/.00491666... = 101577.21

solve for q

c) and d) are invalid questions, since it asks you to add up values of money which are not in the same time spot.
However, if in your course the instructor would accept 540*\$536.2846, go ahead and do it. In terms of actuarial mathematics it would be a bogus result.

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Reiny

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