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Find the monthly payment for the loan.

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3 Answers

128,000 * 0.80 = 102 400 amount of finance.
102,400 * (1 + 0.08/12) ^360 = 1119818. 72 ( 1)
 1119818.72 *( 1- 0.08/12) ^ 360 = 30048.15 (2)
 ( 1119818.72 - 30048.15 )/ 360 = 279.92 (3)
  Financier first calculate the balance of loan with the condition given 0.08 monthly invested for 30 years.
   Then evaluate amount of loan owned at year 30.
    Evaluation of slope between 2 points of amount of loan and amount due at year 30, (3) becomes monthly payment.
The problem we have here is that without knowing what class this is for, and what method they want you to use to solve it, it could be solved several different ways - it would be difficult to show all ways.
The typical tables that are used for accounting and finance classes would not work for something with 360 payments.  (12 montly payments x 30 years = 360 payments.)  Most textbooks just don't include something going as high as 360.
Business math books usually have a special table made just for monthly loan payments, and since only mortgages are likely to be 30 years, there's probably a table just for mortgages that go in 5 year increments.  You just take the amount on the chart and multiply by the amount financed.
You can also use a financial calculator, and you can use the PMT formula in Excel.  And there's also an algebra formula for this.
Regardless of the method, though, you do need to calculate 20% of the loan as the down payment and subtract that off to find out how much is being financed. 
Excel is going to want interest as .085/12 (i.e. interest for the period), a financial calculator or chart will want it kept at 8.5%, not divided down, and not turned into a decimal version.  Excel and financial calculator are going to want N which = 360.  (Total number of payments.)  And I'm not even going to broach the algebra equation unless I know someone needs it.
As you can see, there's several ways to solve these, and each requires the information in different types of formats. 
A $128,000 home bought with a 20% down payment and the balance financed for 30 years at 8.5%. Find the monthly payment for the loan. (Round your answer to the nearest cent.)

P = 128000
D = down payment = P/5
n = 30 yrs * 12 mo/yr = 360 months
r = rate / yr = 0.085
m = monthly payment

month balance
   0       P-D = 4P/5 = B0
   1       B0(1+r/12)-m = B1
   2       B1(1+r/12)-m = B2
 360     B359(1+r/12)-m = B360 = 0

An easy way to solve this is numerically with a spreadsheet like Microsoft Excel ($$$) or LibreOffice Calc (free), and use the Goal Seek Tool.

Here’s a spreadsheet:

The answer is m = $787.37 is the monthly payment.


Thanks so much for your help Steve. I really appreciate it. By chance could you help me figure out this one below? Much Appreciated.
If $36,500 is invested at 6.8% for 30 years, find the future value if the interest is compounded the following ways. (Round your answers to the nearest cent.)
(a) Annually

(b) Semiannually

(c) Quarterly

(d) Monthly

(e) Daily

(f) every minute (N = 525,600)

(g) continuously

(h) simple (not compounded)