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A family has a $150,000, 30-year mortgage at 6.1% com- pounded monthly. Find the monthly payment. Also find the unpaid balanc

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Answer #1
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PMT= PV*i
1-(1+i)^-n
PMT= Monthly payment ?
PV= Loan amount 150,000.00
n= no. of payments 30*12= 360
i 6.1%/12 0.00508333
PMT 150000*0.00508333333333333
1-(1+0.00508333333333333)^-360
PMT 762.5
1-(1.00508333333333333)^-360
PMT 762.5
1-0.161158898627006
PMT 762.5
0.838841101
PMT 908.99 Ans to 1
So monthly payment is $ 908.99.
Remaining balance of loan:
FV= PV(1+i)^n- P(1+i)^n-1)/n
Answer a
PMT= Remaining balance of loan: ?
PV= Loan amount 150,000.00
P= Monthly payment          908.99
n= no. of payments 10*12= 120
i 6.1%/12 0.00508333
FV= 150000*(1+0.00508333333333333)^120- 908.99(1+0.00508333333333333)^120-1)/0.00508333333333333
FV= 150000*(1.00508333333333333)^120- 908.99(1.00508333333333333)^120-1)/0.00508333333333333
FV= 275638.468873644- 908.99*(1.83758979249096-1)/0.00508333333333333
FV= 275638.468873644- 908.99*0.83758979249096/0.00508333333333333
FV= 275638.468873644- 908.99*164.771762457238
FV= 275638.468873644- 149775.884356005
FV=               125,862.58
Remaining balance after 10 years is $ 125,862.58.
Answer b
PMT= Remaining balance of loan: ?
PV= Loan amount 150,000.00
P= Monthly payment          908.99
n= no. of payments 20*12= 240
i 6.1%/12 0.00508333
FV= 150000*(1+0.00508333333333333)^240- 908.99(1+0.00508333333333333)^240-1)/0.00508333333333333
FV= 150000*(1.00508333333333333)^240- 908.99(1.00508333333333333)^240-1)/0.00508333333333333
FV= 506510.436820045- 908.99*(3.37673624546697-1)/0.00508333333333333
FV= 506510.436820045- 908.99*(2.37673624546697)/0.00508333333333333
FV= 506510.436820045- 908.99*(2.37673624546697)/0.00508333333333333
FV= 506510.436820045- 425002.520609906
FV=                 81,507.92
Remaining balance after 20 years is $ 81,507.92.
Answer c
PMT= Remaining balance of loan: ?
PV= Loan amount 150,000.00
P= Monthly payment          908.99
n= no. of payments 25*12= 300
i 6.1%/12 0.00508333
FV= 150000*(1+0.00508333333333333)^300- 908.99(1+0.00508333333333333)^300-1)/0.00508333333333333
FV= 150000*(1.00508333333333333)^300- 908.99(1.00508333333333333)^300-1)/0.00508333333333333
FV= 686614.045922839- 908.99*(4.57742697281893-1)/0.00508333333333333
FV= 686614.045922839- 908.99*(3.57742697281893)/0.00508333333333333
FV= 686614.045922839- 908.99*703.756125800446
FV= 686614.045922839- 639708.813796228
FV=                 46,905.23
Remaining balance after 25 years is $ 46,905.23.
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