Question

A $104,000 selling price with $24,000 down at 8 1/2 for 25 years results in a monthly payment of? I need to kinow how to arrive at the answer.

Answer 1

The key is to sum a geometric series.

Let's just say the Payment is "P".
i = 0.85
These are usually monthly, so j = i/12 = 0.0070833333....
Monthly Discount is v = 1/(1+j) = 0.992966488

At the time of the loan, we have this:

The value of the 1st payment, one month after issue, is Pv
The value of the 2nd payment, two months after issue, is Pv^2

Do you see that this is so?

The value of the 300th payment, 25 years (300 months) after issue, is Pv^300

Do you see the ENTIRE payment stream with its present value at the time of loan origination?

Answer 2

* i = 0.085

Answer 3

How would I arrive at the monthly payment? My choices are $644.80, $654.60, $645.60 & $545.06. Every way I work it, I do not arrive at any of these numbers. So I am missing something in my equation.

Answer 4

And no, I do not see the entire payment stream. This is a hypothetical question.

Answer 5

This is not a hypothetical question. This is where the formulas come from.

If the payment is $100, then we have this stream of payments...

100v + 100v^2 + 100v^3 + 100v^4 + 100v^5 + ... + 100v^last

The exponents represent months. Does this seem to describe a stream of payments to pay back a loan?

Answer 6

You have a choice.

Pick the right equation.
Create the right equation.

Either way will do just fine.

If you used an equation, it would be brilliant to provide the equation you used and how you used it.

Answer 7

"Every way I work it, I do not arrive at any of these numbers. "

can you show us the ways that you are trying to work it?

Answer 8

Here is the question: A $104,000 selling price with $24,000 down at 8 1/2% for 25 years results in a monthly payment of: (A) $644.80, (B) $654.60, (C) $645.60, (D) $546.06

Answer 9

I have minused the down payment and have arrived at an $80,000 dollar balance, multiplied that by 8.50% to arrive at an interest of $6800. Added that to the total & divided by 25 and my figure is way off. So clearly I am NOT doing something right and I am really frustrated.

Answer 10

the interest compounds ... its not the interest for one year either ...

Answer 11

your approach is not conventional by any means ....

80000(1+.085/12)^(12*15)

this is the amount that needs to be compensated for; not 80000(.085)

Answer 12

**** (1+.085/12)^(12*25)

Answer 13

Okay, that is starting to make more sense to me.

Answer 14

the payment structure, as tk was alluding to is a geometric sum of payments

so when the payment structure balances out/compensates for the compounding loan .. we can determine the value.

lets clean it up by saying k=(1+.085/12)

\[80000~k^{12*25}=P\frac{k-1}{k^{12*25}-1}\]
solving for P is then rather elementray

Answer 15

Okay, thanks. This is helpful.

Answer 16

youre welcome, if you want to see why the payment structure is a geometric sum ... id have to find a link to another post where ive worked it out soo many times.

http://openstudy.com/study#/updates/515b2ae2e4b07077e0c16893

wow, 2 years ago i was figuring it out at least lol theres more recent one but this might provide the insights.

Answer 17

http://openstudy.com/study#/updates/51db1b84e4b0d9a104d9737c

same basic explanantion but it might be more readable ...

anywhos, good luck :)