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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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