Question

Jacob has purchased a $129,000 home with a 30-year mortgage at 5.15%. He can make a monthly payment of $1000. If he were to make this payment each month, how many months will it take him to pay off his mortgage? Round your answer to a whole number.

Answer 1

Is it compound interest?

Answer 2

I have no idea. Thats all it says. D:

Answer 3

@kotasoku are you familiar with the mortage formula and the compound interest formulas?

Answer 4

I am not

Answer 5

If you are not familiar with the subject, why would you be doing this exercise?

Answer 6

Maybe it's a real life scenario and s/he is getting ripped off?

Answer 7

lol. But yeah i recieved paperwork with this quesiton and i am struggling on it

Answer 8

Trick question. If it's a 30 year mortgage then you will pay it in 360 months.

Answer 9

For compound interest formula explained:
https://qrc.depaul.edu/StudyGuide2009/Notes/Savings%20Accounts/Compound%20Interest.htm

and mortgage formula explained:
http://www.mtgprofessor.com/formulas.htm

There is not a formula that gives you the solution to your problem directly, it will be by trial and error, but done intelligently.

The simplest idea is that you need to accumulate, after n months at A=$1000 a month, the same amount as the P=mortgaged amount (including interest).
FV1=Future Value of total payments=\(A(R^n-1)/(R-1)\)
where R=1+monthly interest = 1+0.0515/12= 1.00429167 approx.
and
FV2=future value of mortgaged amount=PR^n.
n is the number of \(months\) to pay off the mortgage.

You are looking at the value of n that equalizes FV1 and FV2.
They will not likely to be equal, but if you start with FV1<FV2, then you need to continue paying until FV1>FV2.

A good place to start is we know that at $1000 a month, 129000 cannot be repayed before 129 months! So start with 130 months, FV2-FV1=$51518, then you need to pay at least another 51 months, and so on!

Answer 10

Here is the loan payment formula solved for months:
and a link:
http://www.1728.org/loanfrm3.htm

Answer 11

Still having trouble with this problem. If possible can you tell me what each number is suppose to go into the formula?

Answer 12

Months = log (1+[rate/(Pmt/Princ)-rate] / log (1 + rate)
rate = 5.15/1,200 = 0.0042916667
Months = log (1 + [0.0042916667/(1,000/129,000) -0.0042916667] / log(1+rate)
Months = log ( 1 + 0.0042916667/ ((0.007751938 -0.0042916667) / log (1+rate)
Months = log ( 1 + (0.0042916667/0.0034602713))/ log (1+rate)
Months = log (1 + 1.2402688483) / log (1 + rate)
Months = log (2.2402688483) / log (1+0.0042916667)
Months = 0.3503001399 / 0.0018598591
Months = 188.3476763912

Years = 15.6956396993

Answer 13

Note that the rate for that formula is not 5.15 but 5.15/1,200 = 0.0042916667

Answer 14

thanks i got it

Answer 15

very good - that is a VERY tricky formula !!

Answer 16

@kotasoku
I suggest you take note of the formula, it may be useful for the rest of your academic or work career.
If you do forget or lose track of it, you can still get it back by equating the compound interest formula and the mortgage formula:
P(1+rate)^n=A((1+rate)^n-1)/rate
expand and solve for n to get
n=log(A/(A-P*r))/log(1+r)
A=monthly payment,
r=monthly interest (in decimal)
P=mortgaged amount
n=number of months to pay.
In this case, A=1000, P=129000, r=0.0515/12=0.0042916667
and I get 188.3476795 months