Loan Payment Formula - Years


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

Here, the loan formula has been solved for months.

As you can see from the above formula, solving for months is a bit trickier than solving for monthly payment or principal.

We need to take a loan for $50,000 and we can afford to pay $800.00 per month. The local bank charges 9 per cent interest. How much time will it take to repay this loan?

1) The rate would be 9 ÷ 1,200 = .0075
2) The principal is $50,000.00
3) The monthly payment is $800.00
4) To calculate the time (in months) to repay the loan:

Let's start with the middle of the numerator of the formula.
payment / principal = 800.00 / 50,000.00 = .016
subtracting the rate from this number = (.016 - .0075) = .0085
dividing rate by this number = (.0075 / .0085) = 0.88235294117647
then adding 1 = 1.88235294117647
log (1.88235294117647) = 0.274701056941632

Calculating the denominator is pretty simple
log (1 + rate) = log (1.0075) = 0.00324505481314708

0.274701056941632 / 0.00324505481314708 =
84.6522085940436 months

= 7.0543507161703 years

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