Jingfei bought a house 5 years ago for $350,000. Her down payment on the house was the minimum required 10% at that time she financed the remainder with a 15-year fixed rate mortgage. The annual interest rate was 9% and she was required to make monthly payments, and she has just made her 60th payment. A new bank has offered to refinance the remaining balance on Jingfei's loan and she will have to pay $3,230 per month for the next 10 years, but the total fees she will have to pay today to get the new loan is $1,000. Should she take the new offer? How much will she gain or lose in today's dollars if she does? Annual interest rates are still 9%.

Question

mathhelper · Answer

First of all, I will assume that the 9% was compounded monthly, or else
our standard formulas are not valid, so
i = .09/12 = 0075
actual mortgage = .90(350000) = 315000
n = 15*12 = 180
payment = p
p(1 - 1.0075^-180 )/.0075 = 315000
p = 3,194.94 <---- original monthly payment

So this done for 60 payments

Outstanding balance after 60 payments of this
= 315000(1.0075)^60 - 3194.94(1.0075^60 - 1)/.0075
= 252,213.93
cost of new plan = 1000
so new mortgage = 253,213.93
n = 120
i = still .0075
newpayment = np
np(1 - 1.0075^-120)/.0075 = 253213.93
np = 3207.61

So, what is your conclusion ?
remember if she does not take it, the payment stays at $3,194.94
Looks like a no brainer to me