Loan Payment Formula

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Where rate = Annual Percentage Rate divided by 1200
For example, an 8 % annual rate becomes .0066666666666666...

Let's suppose we want to borrow $150,000 for 30 years at 8 per cent annual percentage rate. What is the monthly payment?

1) The rate would be .0066666666...
2) The months would be 12 × 30 = 360.
3) So the monthly Payment would be:

            .0066666666        
.0066666666   +   ((1.0066666666 ^360)-1)       ×   $150,000

4) The middle section of the equation is the most difficult to solve so we will calculate that first.

(.0066666666) ÷ ((1.0066666666 ^360)-1) =

(.0066666666) ÷ (10.935729397036 -1) =

(.0066666666) ÷ 9.935729397036 =

0.0006709790897

5) "Plugging" this into the rest of the equation we have:
(.0066666666   +   0.0006709790897) × $150,000 =

(0.007337645756) × $150,000 =

$ 1,100.65

Aren't you glad you have the Loan Calculator to use instead of this method?

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