# Math

Dave takes out a 24-year mortgage of 290000 dollars for his new house. Dave gets an interest rate of 14.4 percent compounded monthly. He agrees to make equal monthly payments, the first coming in one month. After making the 68th payment, Dave wants to buy a boat, so he wants to refinance his house to reduce his monthly payment by 500 dollars, and to get a better interest rate. In particular, he negotiates a new rate of 7.2 percent compounded monthly, and agrees to make equal monthly payments (each 500 dollars less than his original payments) for as long as necessary, followed by a single smaller payment. How large will Dave's final loan payment be?

I knew there was a similar question,but I still cannot understand how to calculate.

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1. first contract:
i = .144/12 = .012
n = 24(12) =288
PV = 290000
paym = ?

paym( 1 - 1.012^-288)/.012 = 290000
= ...... -----> X

After making the 68th payment,
balance of loan = 29000(1.012)^68 - X( 1.012^6868 = - 1)/.012
= ...... Y

This becomes the PV of a new contract,
with
new paym = X - 500
i = .072/12 = ..006
n = 288-68 = 220

We don't know how many payments , (periods), we need, let that be n

(X-500( 1 - 1.006^-n)/.006 ) = Y

more than likely, n will be a decimal.
Do not round up, round down
e.g. suppose n = 34.8
you will have to make 34 full payments of (X-500) and a partial paiment at period 35

Have fun

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