Mario obtains a 30/7 balloon mortgage to finance $245,500 at 5.25%. How much principal and interest will he have already paid when his balloon payment is due?

Question

anonymous · Answer

What is a balloon mortgage?

amistre64 · Answer

you need to determine the payment amount

amistre64 · Answer

if we take out a 30 year mortgage for that much at that rate, what will our payments be per month?

anonymous · Answer

what does 30/7 stand for?

amistre64 · Answer

30 year factor to be paid over 7 years, after 7 years the balloon (remainder) is due

anonymous · Answer

ahhh interesting.
Thanks

amistre64 · Answer

yep

amistre64 · Answer

Bn = 245500 k^n - P(1-k^n)/(1-k)

the balance left over after n periods of payments can be calculated with this formula.

solving for Bn = 0 at a period of 30*12 periods allows us to determine the payment amount

amistre64 · Answer

7*12 payments gives us amount of principal and interest that has already been paid

amistre64 · Answer

0 = 245500 k^(360) - P(1-k^(360))/(1-k)

245500 k^(360) = P(1-k^(360))/(1-k)

245500 k^(360) (1-k)/(1-k^(360)) = P

amistre64 · Answer

k is a clean up variable that makes the thing more readable, its the compounding stuff:

k = 1 + rate/12

amistre64 · Answer

245500 k^(360) (1-k)/(1-k^(360)), k=1+.0525/12 http://www.wolframalpha.com/input/?i=245500+k%5E%28360%29+%281-k%29%2F%281-k%5E%28360%29%29%2C+k%3D1%2B.0525%2F12 so our payments are about 1355.66 a month, for 7*12 months