You plan to take out a 30-year fixed rate mortgage for $125,000. Let P(r) be you

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(5)=671.03 and (b) Upper P prime left P(5)=76.39.

(a) Interpret P(5)=671.03.

Select the correct answer below.

A. If the interest rate on the mortgage is 5%, the monthly payment will be $671.03.

B. If the interest rate on the mortgage is 6%, the monthly payment will be $76.39.

C. If the interest rate on the mortgage is 6%, the monthly payment will be $671.03.

D. If the interest rate on the mortgage is 5%, the monthly payment will be $76.39.

(b) Interpret Upper P prime left (5) =76.39.

Select the correct answer below.

A. If the interest rate increases from 5% to 6%, the monthly payment will decrease by approximately $76.39.

B. If the interest rate decreases from 6% to 5%, the monthly payment will be approximately $671.03.

C. If the interest rate increases from 5% to 6%, the monthly payment will increase by approximately $76.39.

D. If the interest rate decreases from 6% to 5%, the monthly payment will increase by approximately $671.03.

Explanation / Answer

Value of the mortgage is $125000

No. of years = 30years

No. of Months = 30*12= 360months

Again, Equated Monthly Installments = Value of the mortgage/ PVIFA (360, r %)

Now if the rate of interest is 5%, then monthly rate = 5%/12= 0.4167%

Or, EMI = 125000/ PVIFA (360, 0.4167%)

Again PVIFA = {1-1/ (1+r) ^n}/r

Or, PVIFA = {1-1/(1.004167)^360}/0.004167= 186.27

EMI = 125000/186.27= $671.07

Again if the rate of interest shifts to 6% from 5%,

Then monthly rate would become (6%/12= 0.5%)

Or, EMI = 125000/ pvifa (360, 0.5%)

Again PVIFA = {1-1/ (1+r) ^n}/r

Or, PVIFA = {1-1/(1.005)^360}/0.005= 166.80

EMI = 125000/166.792= $749.40

So, if the rate of interest increases from 6% from 5% the installments would increase by $78.33 (nearest being $76.39)

Thus in the first case correct answer is option (A), where monthly installments is $671.03 when interest rate is 5% while in the second case correct option is option (C) where monthly installments increases by $78.33 (nearest being $76.39) when rate of interest increases from 5% to 6%.

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