Question

You plan to take out a​ 30-year fixed rate mortgage for ​$125,000. Let​ P(r) be your monthly payment if the interest rate is​ r% per​ year, compounded monthly. Interpret the equations

​(a) ​P(7​)=831.63.select the correct answer bellow

A) If the interest rate on the mortgage is 8​%, the monthly payment will be ​$83.95.

B) If the interest rate on the mortgage is 7​%, the monthly payment will be ​$831.63.

C) If the interest rate on the mortgage is 8​%, the monthly payment will be ​$831.63.

D) If the interest rate on the mortgage is 7​%, the monthly payment will be ​$83.95.

(b) Interpret P'(7)=83,95.Select the correct answer

A) If the interest rate decreases from 8​% to 7​%, the monthly payment will increase by approximately ​$831.63.

B) If the interest rate increases from 7​% to 8​%, the monthly payment will decrease by approximately ​$83.95.

C) If the interest rate increases from 7​% to 8​%, the monthly payment will increase by approximately ​$83.95.

D) If the interest rate decreases from 8​% to 7​%, the monthly payment will be approximately ​$831.63.

Answer 1

GIven that p(r) is the monthly payment, if the interest is r% per year ==> If the interest rate for the mortgage is r%, the monthly payment is p(r)

Let's interpret p(7) = 831.63 ==> If the interest rate for the mortgage is 7%, the monthly payment is 831.63

* If the interest rate increases, the monthly payments also increase. both are directly proportional.

So, based on this logic, in the second question, we can say that, if the interest rate increase from 7% to 8%, the monthly payments increase by 83.95.