Question

You plan to take out a 30-year fixed rate mortgage for $225,000. Let PC) be your monthly payment if the interest rate is r% per year, compounded monthly. Interpret the equations (a) P(6) = 1348.99 and (b)P (6) = 144.66. (a) Interpret P(6) = 1348.99. Select the correct answer below. O A. If the interest rate on the mortgage is 7%, the monthly payment will be $1348.99. OB. If the interest rate on the mortgage is 6%, the monthly payment will be $1348.99 OC. If the interest rate on the mortgage is 7%, the monthly payment will be $144.66. OD. If the interest rate on the mortgage is 6%, the monthly payment will be $144.66. (b) Interpret P (6) = 144.66. Select the correct answer below. O A. If the interest rate decreases from 7% to 6%, the monthly payment will increase by approximately $1348.99. OB. If the interest rate increases from 6% to 7%, the monthly payment will increase by approximately $144.66. OC. If the interest rate increases from 6% to 7%, the monthly payment will decrease by approximately $144.66. OD. If the interest rate decreases from 7% to 6%, the monthly payment will be approximately $1348.99.

Answer 1

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Answer:

Value of the mortgage is $225000

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 6%, then monthly rate = 6%/12= 0.5%

Or, EMI = 225000/ PVIFA (360, 0.5%)

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

Or, PVIFA = {1-1/(1.005)^360}/0.005= 166.7916

EMI = 225000/166.7916= $1348.988

Again if the rate of interest shifts to 6% from 7%,

Then monthly rate would become (7%/12= 0.5833%)

Or, EMI = 225000/ pvifa (360, 0.5833%)

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

Or, PVIFA = {1-1/(1.0058333)^360}/0.0058333= 150.3082

EMI = 225000/150.3082= $1496.924319

So, if the rate of interest increases from 6% from 7% the installments would increase by $147.936

Hence for question 1 option is B

and for question 2 is option B