Question

Kathy is financing $218,675 to purchase a house. She obtained a 30/10 balloon mortgage at 3.35%. What will her balloon payment be?

$174,042.89
$152,249.65
$168,871.56
$168,401.44
@amistre64

Answer 1

@Michele_Laino

Answer 2

omg are you taking the final right now?!

Answer 3

adv alg with financial application?

Answer 4

ok, so tell me what your understanding of a balloon payment is

Answer 5

yep

Answer 6

the balloon payment has a lower price at first but after the end a large sum is owed from the loan

Answer 7

@amistre64

Answer 8

this question is about a 30/10 so its a 30 year mortgage

Answer 9

balloon payment is just a payment, its the final payment we need to make.

Answer 10

we make 10 years of monthly payments calculated on a 30 year loan

whats our normal monthly payments on a 30 year loan?

Answer 11

for a normla 30 year mortgage it would be 607.430

Answer 12

thats not what i get for a monthly payment

i have a formula that I developed

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

for n compounding periods (30*12) = 360 we want the loan paid off, B{360} = 0

\[0=Bk^{360}-P\frac{k^{360}-1}{k-1}\]
we can solve for P
\[Bk^{360}\frac{k-1}{k^{360}-1}=P\]
k is our compounding stuff, k = 1+.0335/12

and B is our initial loan amount

Answer 13

http://www.wolframalpha.com/input/?i=218675%281%2B.0335%2F12%29%5E%2830*12%29+%281%2B.0335%2F12-1%29%2F%28%281%2B.0335%2F12%29%5E%2830*12%29-1%29

Answer 14

i got 360 i was spreading that over the loan amount for individual payments... what did you get?

Answer 15

P = 963.73

Answer 16

yeah, your monthly payment approach is invalid. we have to deal with interest so dividing the loan amount by 360 is not appropriate

Answer 17

now what we need, is the balance on the loan after we make 10*12 - 1 payments

120 payment make up all of the payments, 119 are regular monthly payments, and the last one is a balloon, it is the compounded balance after that 119th payment was sent in.

Answer 18

oh, ok, so how do we figure that

Answer 19

i gave you how I figure out a monthly payment with a formula i derived for it. now the ballon uses the same formula, but with the relevant information

\[B_{119}=Bk^{119}-P\frac{k-1}{k^{119}-1}\]
\[Balloon=B_{119}k\color{red}{\implies} Bk^{120}-Pk\frac{k-1}{k^{119}-1}\]

Answer 20

you need to know how to find a monthly payment, im concerned that you dont know that yet.

Answer 21

ugh, i got my geometric sum on my ballon payment flipped over.

k^n -1 should be on top

\[B_{119}=Bk^{119}-P\frac{k^{119}-1}{k-1}\]
balloon is still B{119} * k of course

Answer 22

so i use the formula you gave me with the info im given from my question then

Answer 23

thats how i work it yes

Answer 24

do i change b?

Answer 25

how your material works it is another story :)

Answer 26

in this formula what is K?

Answer 27

B defines your loan amount.

Bn defines the balance onthe loan

Answer 28

and as stated earlier, k is the compounding rate ... re-read the posts

Answer 29

right sorry

Answer 30

so here is what i think i have P=963.73 B=218,675 BN=3.35% K=10 is any of the right

Answer 31

P and B are right :)

k = 1 + .0335/12

Bn is just a balance after n = (10*12-1) periods

Answer 32

now the issue i have is that my solution is not an option. so im going to double check this with an online calculation

Answer 33

http://tcalc.timevalue.com/all-financial-calculators/mortgage-calculators/balloon-mortgage-calculator.aspx?PRINCIPALAMOUNT=218675&DOWNPAYMENTAMOUNT=0&DOWNPAYMENTAMOUNT_TYPE=Percent&TERM=30&TERM_UNITS=Years&BALLOONPAYMENTAFTER=10&BALLOONPAYMENTAFTER_UNITS=Years&INTERESTRATE=3.35+%25&COMPUTE=COMPUTE&SHOWAMORTIZATIONSCHEDULE=on&CALCULATORID=HF04&HIDEFORMTAG=TRUE&TEMPLATE_ID=www.timevaluecalculators.com_1&PostBack=true#results

Answer 34

ok i can see how that works

Answer 35

119th monthly payment is

218675k^(10*12-1)-963.73(k^(10*12-1)-1)/(k-1) = 168 893. 73

which is only 3 cents off of the online calculator
-----------------------------------

my balloon is 169 365. 22 which is just a few cents off of the online as well

none of your options fit this.

Answer 36

i can see... ill try my teacher