2021-03-11-project 4 Han Zhang .ipynb

Kernel: Python 3 (system-wide)

x=1+0.052/12
c=-208000*(x**360)*(1-x)/(1-x**360)
c

-1142.150632443497

for original 30 years with rate 5.2% , monthly payment is 1142.1506

1142.1506*360-208000

203174.21599999996

for 30 years , the owner should pay total interests is 203174.216 

p=208000*(x**120)-1142.15*(1-x**120)/(1-x)
p

170202.578411025

now we count the refinance option , after the first ten years original loan, there are 170202.578 left

x=1+0.039/12
C=(12000-(170202.578)*(x**360))*(1-x)/(1-x**360)
C

-785.1912588058652

for additional 30 years , the owner should pay $785.19 per month

1142.1506*120+785.191*30*12-208000+12000

223726.832

then 40 years for the interests , the owner should pay 223726.832. compare with 30 years ($203174.216), I THOUGHT THE REFINANCE OPTION IS WORTHWHILE BECAUSE IT IS NOT A BIG DIFFERENCE IN THE INTERESTS BUT EXTRA 10 YEARS COULD BE CONTINUED AND EVERYMONTH PAY LESS THEN THE 30 YEARS . SO I WILL CHOOSE REFINANCE OPTION.

The $12,000 is not part of the principal sum for the refinance option, but that is besides the point. You gave the $12,000 the wrong sign, making your monthly payment smaller than expected. Be sure to include an introduction to the problem at the top of your document. What are you trying to solve? 9/10

x=1+0.167/12
c=-3500*x**12*(1-x)/(1-x**12)
c

-318.71854813021145

3500*x**12/12

344.2817028530176

3500*0.167/12

48.708333333333336

x=1+0.082/12
c=20000*x**48*(1-x)/(1-x**48)
c

490.1382323808376

x=1+0.042/12
c=250000*x**360*(1-x)/(1-x**360)
c

1222.5429342838258

1222.54*360

440114.39999999997

440114.4-250000

190114.40000000002