Question

Ms. Juliet bought a house for $360,000 exactly five years ago. After making a 20% down-payment, she borrowed the rest of the house payment in the form of a 15-year mortgage from her local cooperative credit union. She negotiated a mortgage rate of 3.5% APR with semi-annual compounding. She makes mortgage payments of an equal dollar amount every two weeks (i.e., biweekly), and her first mortgage payment was due two weeks after she signed the mortgage contract.

d. What is her current mortgage balance?

Answer 1

Annual interest rate of 3.5% compounded semi annually is equivalent to biweekly rate of 0.13354%, as follows:

8 L =((1+C5)^(1/C8))-1 B A с 1 Given Given 1 2 Yearly Nominal Rate (R) 3 Compounding frequency 4 Times compounded a year (t) 5 EAR=((1+R/t)^t)-1 6 7 Frequency 8 Times compounded a year (t) 9 Biweekly rate rate 3.5% Semi annually 2 3.5306% ((1+C2/C4)^C4)-1 Bi weekly 26 0.13354% ((1+C5)^1/08)-1

Principal outstanding after payment for 5 years= $208,093.73

Calculation as follows:

D13 c =PV(D2,D12,010,08,09)*-1 A B C D Function 1 Formula arguments Values 2 Interest rate per period As above Rate 0.133540% 3 Number of years total (N) Given 15 4 Frequency of payments Given Biweekly 5 Number of payments a year (t) 26 6 Total number of payments N*t Nper 390 7 Loan amount 360000*(1-20%) Pv $ 288,000.00 8 Future Value FV 0 9 Timing of payment (End of period) Given Type 0 10 Periodical payment PMT(D2,D6,07*-1,D8,09) PMT $ 947.86 11 Number of payments made 5 Years* 26 130 12 Number of future payments D6-D11 Nper 260 13 Principal outstanding PV(D2,D12,D10,D8,09) PV $208,093.73