Question

Karen is financing $291,875 to purchase a house. She obtained a 15/5 balloon mortgage at 5.35%. What will her balloon payment be?

Answer 1

So what I know is that the 15 means it'll be paid like it's going to be paid off in 15 years. However, they make those payments for 5 years since it's a 15/5. The remaining amount has tax added somewhere and then the remaining is the balloon. @rational

Answer 2

Found something to work with for the monthly payment calculation

Answer 3

you want to calculate monthly payment as if it is a 15 year loan ?

Answer 4

Yes, but they pay it for 5 years

Answer 5

Once we have the amount they paid over 5 years, we subtract that from the original amount.

Answer 6

gotcha lets calculate monthly payment first then

Answer 7

Yeah, once we have that the rest comes together pretty simply from what I can tell

Answer 8

Monthly payment :
https://www.wolframalpha.com/input/?i=291875*0.0535%2F12*%281%2B0.0535%2F12%29%5E%2812*15%29%2F%28%281%2B0.0535%2F12%29%5E%2812*15%29-1%29

Answer 9

do we need to multiply it by 12*5 to get the amount paid ?

Answer 10

Here is the amount paid in 5 years
https://www.wolframalpha.com/input/?i=%28291875*0.0535%2F12*%281%2B0.0535%2F12%29%5E%2812*15%29%2F%28%281%2B0.0535%2F12%29%5E%2812*15%29-1%29%29*12*5

Answer 11

2361.69 * 60 = 141,701.40

Answer 12

Next we subtract that from the original mortgage

Answer 13

$291,875 - 141,701.60 = $150,173.40

Answer 14

that may not work, as "141,701.40" includes interest also.

Answer 15

we dont make a full 5 years of payments, we make 1 less

Answer 16

I believe its 5 years

Answer 17

After you find the difference of original mortgage and payments made, my lesson says to apply one month's interest to the remaining and then you have the remaining balloon.

Answer 18

payments are a geometric progression:

P(k^n-1)/(k-1) defines the value of all payments made with respect to accruing interest

the balance of the loan if Bk^n

when the compounding loan is balanace by the payments, we have the loan paid off

\[Bk^n=P\frac{k^n-1}{k-1}\]
monthly payment P is just
\[P=Bk^n\frac{k-1}{k^n-1}\]

Answer 19

P = 291875k^(15*12) (k-1)/(k^(15*12)-1), k=1+.0535/12

Answer 20

http://www.wolframalpha.com/input/?i=291875k%5E%2815*12%29+%28k-1%29%2F%28k%5E%2815*12%29-1%29%2C+k%3D1%2B.0535%2F12

P = 2361.69

Answer 21

5*12 - 1 is the number of regular monthly payments, the remainder the ballon, is the final 60th payment

Answer 22

recall that Bn=0 defines the ending balance, therefore
\[B_n=Bk^n-P\frac{k^n-1}{k-1}\]
\(B_{59}\) is our next to last payment, and then interest accrues for one more month

\(B_{59}~k\) is our ballon payment

Answer 23

any of this make sense?

Answer 24

B0 = B , we take out a loan

B1 = Bk - P , interest accrues and we make a payment

B2 = B1 k - P , interest accrues and we make a payment
= (Bk - P)k - P
= Bk^2 - P - Pk

B3 = B2 k - P , interest accrues and we make a payment
= (Bk^2 - P - Pk)k - P
= Bk^3 - P - Pk - Pk^2

.....

Bn = Bk^n - P(sum of a geometric sequence in k)

Answer 25

when Bn = 0

0 = Bk^n - P(k^n-1)/(k-1)

Bk^n = P(k^n-1)/(k-1)

which is what i stated at the begining to define payment amounts

Answer 26

https://www.wolframalpha.com/input/?i=%28291875*%28%281%2B0.0535%2F12%29%5E%2812*15%29-%281%2B0.0535%2F12%29%5E%2812*5%29%29%2F%28%281%2B0.0535%2F12%29%5E%2812*15%29-1%29%29*%281%2B0.0535%2F12%29

Answer 27

Does this seem correct?

Answer 28

im just wondering how your formula for payment coincides with the common PV payment formula
\[P=\frac{PV*r}{1-(1+r)^{-n}}\]

Answer 29

I see how you derived your formula ... and I know how this formula is derived
But do they actually equal each other ? Or are they diff formulas?

Answer 30

B_59 = 291875k^(59) - (2361.69)(k^59-1)/(k-1), k=1+.0535/12

B_59 = 220491.35

B_60 = B_59 k = ballon payment

Answer 31

they are equal, i just hate the textbook version of it, it doesnt convey the mechanics of it and relies to heavily on trying to memorize a format

Answer 32

oh ok cool

Answer 33

PV is a tabled value isnt it ....

Answer 34

i use my formula to find many many things that my accounting classes kept trying to give different formulas for ... why learn 12 different things, when 1 will do fine?

Answer 35

LOL I guess so
But the otehr derivation is very helpful when the payments vary every month
or ya wanna find the net Present value

Answer 36

depreciation was a hoot

if there is no salvage value: use cost/life to define straight line depreciation

if we have salvage value: use the formula (cost - salvage)/life

why? why not define it as: (cost - salvage)/life to start with?

Answer 37

i havent tried to generalize it to varying payments yet :) but yeah, that might be a pro for it

Answer 38

on my the tests, while everyone was lookng up tables and trying to find the proper format of the formulas, i was just plugging in values and moving right along lol

Answer 39

LOL i feel like id be the one scrambling for formulas
K can we just clarify the balloon payment method since i am not sure i follow it
So basically you divide the payments as if you were paying it over 15 years
In actuality you only pay for 5 years
Then the remainder of what is left over you pay in one lump sum
Is it the remainder of payments?
Or is the remainder of the loan?

Answer 40

the monthly payments are defined for the usual fixed rate loan of say 15 years

we pay off that loan like usual for 5 years, except for one difference

the next to last payment is the last monthly payment, the 60 payment is the ballon, that amount of the after the last monthly payment, compounded for 1 more month

Answer 41

59P + balloon = total cost of the loan

Answer 42

how much do we save in interest? do we save in interest?

Answer 43

12*15P - principal = interest (on a 15 year loan)

58P + balloon - principal = interest (on a 15/5 )

Answer 44

Its 59 not 58 right?
59P + balloon - principal = interest (on a 15/5 )

Answer 45

12*5 = 60 payments, 59 are monthly, 1 is balloony

Answer 46

yeah, slip of the finger lol

Answer 47

lol okkk

Answer 48

12*15*2361.69 - 291875 = 133229

220491 + 221474 - 291875 = 150090

of course we would expect to pay more in interest for a higher risk loan. it favors the investor.

Answer 49

RIght so less interest with balloon method

Answer 50

nope, more interest

Answer 51

waitttt

Answer 52

the more compounded the less interest

Answer 53

but why wld someone choose this balloon method then -.-

Answer 54

It pays off the mortgage quickly

Answer 55

15 years has a balance after 5 years ... we havent reduced the balance enough to compensate

Answer 56

why does anyone take a higher interest loan? desperation of course

Answer 57

Got stuck on another question dealing with "weighted mean". You guy's willing to help?

Answer 58

link to the post?

Answer 59

K thanks guys ... gonna chew over this

Answer 60

http://openstudy.com/study#/updates/5554dc3ae4b0fb3e4010d33c

Answer 61

@amistre64 I thought about your statement earlier that "more interest is accrued when using the balloon method" and I kinda disagree.

The longer the loan is unpaid the more interest it accrues. Every compounding period we have to pay interest for the amount that is still outstanding. Therefore with the Balloon method you pay less interest.

12*15*2361.69 - 291875 = 133229 --> 15 Year Loan

139339.71 + 221474 - 291875 = 68938.71 ---> Balloon Method

Answer 62

pfft,

220491 was the balance that accrued one more interest for balloon. i used the wrong value ....

i was thinking along the lines that the payments mostly cover interest in the beginning and not so much the principal. I wasnt even thinking that i had an error :)

Answer 63

i do like being proved wrong ;) keeps me learning lol

Answer 64

hahaha You kept me pondering over this alll evening.
Was killing my brain