Question

4. A $180 000.00 mortgage is to be amortized by making monthly payments for 22.5 years. Interest is 7.2% compounded semi-annually for a four-year term. a) Compute the size of the monthly payment. b) Determine the balance at the end of the four-year term. c) If the mortgage is renewed for a five-year term at 8.66% compounded semi- annually, what is the size of the monthly payment for the renewal term?

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

A B C PV Loan Amount Term in years Interest rate (2) Effective monthly interest rate No. of monthly payment $180,000.00 22.5 7.20% 0.591% 270 /Y N PMT Size of Monthly payment $1,336.22 b) 222 N 1/Y PMT Remaining monthly payemnt after Year 4 Effective monthly interest rate Size of Monthly payment 0.591% $1,336.22 PV Balance of loan at end of Year 4 $164,949.97 PV Balance of loan at end of Year 4 Annual interest rate Effective monthly interest rate Term in years No. of monthly payment $164,949.97 8.66% 0.007089809 1/Y N 60 | PMT Size of monthly payment for renewal term $3.384.82 |

Cell reference -

A B D PV Loan Amount Term in years Interest rate (2) Effective monthly interest rate No. of monthly payment 180000 22.5 0.072 =(1+D4/2)^(1/6)-1 =D3*12 1/Y N PMT Size of Monthly payment =PMT(D5,D6,-D2,,0) N 1/Y PMT Remaining monthly payemnt after Year 4 Effective monthly interest rate =C8 =D6-4*12 =D5 =D8 14 PV Balance of loan at end of Year 4 =PV(D11,D10,-D12,,0) 17 c) PV =C14 Annual interest rate Effective monthly interest rate Term in years No. of monthly payment =D14 0.0866 (1+218/2)^(1/6)-1 1/Y N =D20*12 PMT Size of monthly payment for renewal term EPMT(D19,D21-D17..0)

Please note: Assumed- Term renewed at end of Year-4

Hope it will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.