Question

4. Ann obtains a fully amortizing 30 year Fixed Rate Mortgage with annual payments for $135,000 at 5.25%. How much does Ann need to pay annually?

7. Ann obtains a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $135,000 at 5.25%. What will be Ann’s mortgage balance after 20 years of payments (ie after 240 months)?

Answer 1

4. Ann obtains a fully amortizing 30 year Fixed Rate Mortgage with annual payments for $135,000 at 5.25%. How much does Ann need to pay annually?

Finding payment per period:
Asset Value = A	$135,000.00
Down Payment = DP = 0 =	$0.00
P = Principal Loan = (A - DP) =	$135,000.00
R = Rate =	5.25%
N = Numbers of payment =	30
PMT = Payment = P x R x (1+R)^N / ((1+R)^N - 1) =	9,033.79

Formula for calculating payment (working)

PMT = P x R x (1+R)^N / ((1+R)^N - 1)

PMT =135000*5.25%*(1+5.25%)^30/((1+5.25%)^30-1)

PMT = $ 9,033.79 (Rounding to nearest cent or two decimal places)

7. Ann obtains a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $135,000 at 5.25%. What will be Ann’s mortgage balance after 20 years of payments (ie after 240 months)?

Finding outstanding balance at end of the particular time
P = Principal Loan = (A - DP) =	$135,000.00
R = Rate = 5.25%/12 =	0.43750%
n = Total number of payments done =	240
PMT = Payment = P x R x (1+R)^N / ((1+R)^N - 1) =	745.475
FV = Outstanding Balance = (P*(1+R)^n)-(PMT*((1+R)^n-1)/R)	$ 69,481.14

Formula for calculating outstanding balance (working)   

FV = (P*(1+R)^n)-(PMT*((1+R)^n-1)/R)  

FV =(135000*(1+5.25%/12)^240)-(745.475*((1+5.25%/12)^240-1)/(5.25%/12)) = $ 69,481.14 (approx.)