Why \$537 a month for \$100,000 loan, 5% interest, 30-yr term? [duplicate]

Apparently, a \$100,000 loan with an interest rate of 5 percent and a 30-year term carries a payment of \$537 a month.

Why? I've fiddled with the numbers in various ways and can't get \$537. For instance, (\$100,000 * 1.05) / 30 / 12 = \$292 a month.

marked as duplicate by JoeTaxpayer♦Jun 4 '16 at 10:28

Using formula

``````r = 0.05/12
n = 30*12
s = 100000

(r s)/(1 - (1 + r)^-n) = 536.822
``````

Apparently, a \$100,000 loan with an interest rate of 5 percent and a 30-year term carries a payment of \$537 a month.

Why? I've fiddled with the numbers in various ways and can't get \$537. For instance, (\$100,000 * 1.05) / 30 / 12 = \$292 a month.

The biggest error in your formula is that you assumed that the total interest for the loan would be 100,000*0.05 or \$5,000; but that is closer to the interest for the first year. Your formula spread the payment of the first years interest over the 30 years; and then assumed no interest would be charged for the next 29 years.