The formula for calculating monthly payments

Explore MathSome of you have expressed interest in the formula for monthly payments. Here it is.

\begin{array}{l}\text{Monthly Payment}=\frac{rP}{1-{{(1+r)}^{-n}}}\\r=\text{periodic rate=}\frac{\text{annual rate}}{\text{number of periods per year}}\\n=\text{number of periods to pay back loan}\end{array}

You can find the total cost of repaying a loan by multiplying both sides by n, the number of payments to be made.

n\cdot Paymen{{t}_{monthly}}=\frac{rPn}{1-{{(1+r)}^{-n}}}

I hope this will help you all remember that you can’t just plug in the interest rate and some numbers to your calculator to get an answer when finding the cost of repaying loans!

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