Question

Need help in financial applications, please. Joanne and Bill are financing $305,500 to purchase a house. They obtained a 20/6 balloon mortgage at 5.75%. What will their balloon payment be?
$206,311.68
$401,524.25
$152,285.77
$249,295.69

Answer 1

first calculate the monthly payment of a 20 fixed loan at the given rate

Answer 2

use that to calculate the remaining balance due after 6 years of payments

Answer 3

I tend to develop my own formula for this:\[A = Bk^n+P\frac{1-k^n}{1-k}\]
20 years of 12 payments a year = n

B is the starting balance
k is the compounding rate (1+r/12)

when A=0 the loan is paid off so we can solve for P, the payments

\[0 = Bk^n+P\frac{1-k^n}{1-k}\]
\[-Bk^n=P\frac{1-k^n}{1-k}\]
\[-Bk^n\frac{1-k}{1-k^n}=P\]

Answer 4

we can use the same formula after knowing P and let n = 6 years of 12 payments .... to find the remaining balance to pay off

Answer 5

if we want to do some algebra to it ...

\[A = Bk^n+P\frac{1-k^n}{1-k}\]
\[A = Bk^n+(-Bk^n\frac{1-k}{1-k^n})\frac{1-k^m}{1-k}\]
\[A = Bk^n-Bk^n\frac{1-k^m}{1-k^n}\]
\[A = Bk^n(1-\frac{1-k^m}{1-k^n})\]
\[A = Bk^n(\frac{1-k^n-1+k^m}{1-k^n})\]
\[A = Bk^n(\frac{k^m-k^n}{1-k^n})\]
but thats just moving things about

Answer 6

lol, thats why i just use the first stuff

Answer 7

what do you get for your monthly payment?

Answer 8

im getting about 2144.87 for payments and balancing out at about 247k

Answer 9

if they are using tables and not being as exact ... that 249 seems to be the closest due to rounding errors and such. but thats just a hunch

Answer 10

you are too fast. I got 2144.51 for monthly

Answer 11

the wolf helps :)

http://www.wolframalpha.com/input/?i=%28305500%29k%5E%2820*12%29+%5Cfrac%7B1-k%7D%7B1-k%5E%2820*12%29%7D%2C+k%3D%281%2B.0575%2F12%29

Answer 12

or for a table of balances, year 6 is 247k

http://www.wolframalpha.com/input/?i=payment&a=*C.payment-_*Formula.dflt-&a=FSelect_**FixedRateMortgage-.dflt-&f3=305500&f=FixedRateMortgage.MA_305500&f4=20+yr&f=FixedRateMortgage.MP_20+yr&f5=5.75+%25&f=FixedRateMortgage.APR_5.75+%25&a=*FVarOpt.1-_***FixedRateMortgage.MA--.***FixedRateMortgage.SA-.*FixedRateMortgage.DP---.*--&a=*FVarOpt.2-_**-.***FixedRateMortgage.PTS--.**FixedRateMortgage.IOP--.**FixedRateMortgage.MTR--.**FixedRateMortgage.BP---.**FixedRateMortgage.MA---

Answer 13

I got 151894 for the balloon payment. not one of choices

Answer 14

I also have another formula and got 247096 for the balloon payment. I'm confused.