Question

Stephanie finances $423,000 with a 20/5 balloon mortgage at 4.45%. How much will she pay for principal and interest over the life of the loan?
A. $508,077.56
B. $509,378.67
C. $ 510,674.71
D. $505,422.01

Answer 1

Determine the Payments for a fixed morgage of 20 years, balance it out for 5 years, and pay off the remaining balance.

add up all the payments made

Answer 2

a fixed loan can be modeled using this formula:
\[A=-Bk^n+P\frac{1-k^n}{1-k}\]
When A = 0 the loan is paid in full
\[0=-Bk^n+P\frac{1-k^n}{1-k}\]
\[Bk^n=P\frac{1-k^n}{1-k}\]
\[Bk^n\frac{1-k}{1-k^n}=P\]
there are 5(12) payments
\[60*Bk^n\frac{1-k}{1-k^n}=$paid~in~5~years\]
and after 5 years the remianing balance is
\[A=-Bk^{60}+P\frac{1-k^{60}}{1-k}\]

Answer 3

http://www.wolframalpha.com/input/?i=%28423000%29k%5E%2820*12%29%5Cfrac%7B1-k%7D%7B1-k%5E%2820*12%29%7D%3B+k%3D1%2B.0445%2F12

using 20*12 as the number of periods, and k=1+.0445/12 as the compunding interest

Payments are about 2664.70 a month, 5 years gives us a total of 159 882, plus the remaining balance of the loan

Answer 4

http://www.wolframalpha.com/input/?i=-%28423000%29k%5E%7B60%7D%2B%282664.70%29%5Cfrac%7B1-k%5E%7B60%7D%7D%7B1-k%7D%3B+k%3D1%2B.0445%2F12

so there is about 349 497 left to pay off

349 497
159 882
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