Try this find the amount of a 25-year mortgage at 4.2% interest compounded monthly where the monthly payment is $457.06 (do not round until the final answer. then round to the nearest dollar as needed.)

$84,807

Step-by-step explanation:

The appropriate amortization formula is ...

... A = P(r/n)/(1 - (1 +r/n)^(-nt))

where A is the monthly payment, P is the principal amount of the loan (which we want to find), r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

Putting the given information into the formula, we have ...

... 457.06 = P(0.042/12)/(1 -(1 +0.042/12)^(-12·25))

... = P·0.00538942318

Then ...

... P ≈ 457.06/0.00438942318 ≈ 84,806.849

Rounded to the nearest dollar, that is ...

... P ≈ $84,807

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