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Mortgage


Let B dollars be borrowed at an interest rate of i per month, where i is the annual rate divided by 12, and assume the mortgage needs to be paid back in n months. Then the monthly payment is given by

 monthly payment=B×i×((1+i)^n)/((1+i)^n-1).

For example, $100,000 on a 360-month (30-year) mortgage at a monthly rate of .0075 (9% annually) would require a monthly payment of

 $100,000×.0075×(1.0075^(360))/(1.0075^(360)-1)=$804.62.

See also

Compound Interest

This entry contributed by Ed Pegg, Jr. (author's link)

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References

Zwillinger, D. (Ed.). CRC Standard Mathematical Tables and Formulae, 30th ed. Boca Raton: CRC Press, 1996.

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Mortgage

Cite this as:

Pegg, Ed Jr. "Mortgage." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Mortgage.html

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