Question

- Billy McMahon is interested in buying a waterfront condo and
has saved $100,000 for the down payment. His plans call for making
additional monthly deposits into an investment account over the
next 36 months. Billy McMahon wants to make the purchase 48 months
from today and wants to have $180,000 saved up for the down
payment.
- What is the amount of each of the additional payments he must make for his plan to work out? Assume Billy can earn 2% annual return in his investment account.
- If Billy takes out a 30-year, $720,000 mortgage at 4%, what will his mortgage payments be?
- Prepare an amortization schedule to prove that your answer is right and his mortgage will be paid off in 30 years.
- If Billy takes out a 20-year, $720,000 mortgage at 3.5%, what will his mortgage payments be?
- How much would Billy save if he took out a 20-year mortgage versus a 30-year mortgage?

Answer #1

**(a)**

$180000 at the end of 48 months | |||||

=180000/1.02 at the end of 36 months | |||||

(as Billy can earn 2% annual return in his investment account.) | |||||

Therfore, Requirement at the end of 36 months = |
$1,76,470.59 |
||||

Additional Monthly deposits |
$1934.36 |
||||

Month |
Investment |
FV Factor @ 2% p.a |
FV |
||

0 | 100000 | 1.0000 | 100000 | ||

1 | 1934.36 | 1.0050 | 1944.0318 | ||

2 | 1934.36 | 1.0100 | 1953.752 | ||

3 | 1934.36 | 1.0151 | 1963.5207 | ||

4 | 1934.36 | 1.0202 | 1973.3383 | ||

5 | 1934.36 | 1.0253 | 1983.205 | ||

6 | 1934.36 | 1.0304 | 1993.121 | ||

7 | 1934.36 | 1.0355 | 2003.0866 | ||

8 | 1934.36 | 1.0407 | 2013.1021 | ||

9 | 1934.36 | 1.0459 | 2023.1676 | ||

10 | 1934.36 | 1.0511 | 2033.2834 | ||

11 | 1934.36 | 1.0564 | 2043.4498 | ||

12 | 1934.36 | 1.0617 | 2053.6671 | ||

13 | 1934.36 | 1.0670 | 2063.9354 | ||

14 | 1934.36 | 1.0723 | 2074.2551 | ||

15 | 1934.36 | 1.0777 | 2084.6264 | ||

16 | 1934.36 | 1.0831 | 2095.0495 | ||

17 | 1934.36 | 1.0885 | 2105.5248 | ||

18 | 1934.36 | 1.0939 | 2116.0524 | ||

19 | 1934.36 | 1.0994 | 2126.6326 | ||

20 | 1934.36 | 1.1049 | 2137.2658 | ||

21 | 1934.36 | 1.1104 | 2147.9521 | ||

22 | 1934.36 | 1.1160 | 2158.6919 | ||

23 | 1934.36 | 1.1216 | 2169.4854 | ||

24 | 1934.36 | 1.1272 | 2180.3328 | ||

25 | 1934.36 | 1.1328 | 2191.2344 | ||

26 | 1934.36 | 1.1385 | 2202.1906 | ||

27 | 1934.36 | 1.1442 | 2213.2016 | ||

28 | 1934.36 | 1.1499 | 2224.2676 | ||

29 | 1934.36 | 1.1556 | 2235.3889 | ||

30 | 1934.36 | 1.1614 | 2246.5659 | ||

31 | 1934.36 | 1.1672 | 2257.7987 | ||

32 | 1934.36 | 1.1730 | 2269.0877 | ||

33 | 1934.36 | 1.1789 | 2280.4331 | ||

34 | 1934.36 | 1.1848 | 2291.8353 | ||

35 | 1934.36 | 1.1907 | 2303.2945 | ||

36 | 1934.36 | 1.1967 | 2314.8109 | ||

Total |
176470.6 |

Calculation of FV Factor = (1+(0.06/12))^Month No.

Calculation of Monthly Deposit = (176470.59-100000)/aggregate of FV Factors from 1-36 months

**b.**

If Billy takes out a 30-year, $720,000 mortgage at 4%, his mortgage payments will be,

=PMT(4%,30,720000,0,0)=**$41637.67**

**c.**

Year |
Opening Loan |
Interest @ 4% |
Installment |
Principal Repayment |
Closing |

1 | 720000 | 28800 | 41637.67 | 12837.67 | 707162.33 |

2 | 707162.33 | 28286.49 | 41637.67 | 13351.18 | 693811.15 |

3 | 693811.15 | 27752.45 | 41637.67 | 13885.23 | 679925.93 |

4 | 679925.93 | 27197.04 | 41637.67 | 14440.63 | 665485.29 |

5 | 665485.29 | 26619.41 | 41637.67 | 15018.26 | 650467.03 |

6 | 650467.03 | 26018.68 | 41637.67 | 15618.99 | 634848.04 |

7 | 634848.04 | 25393.92 | 41637.67 | 16243.75 | 618604.29 |

8 | 618604.29 | 24744.17 | 41637.67 | 16893.50 | 601710.79 |

9 | 601710.79 | 24068.43 | 41637.67 | 17569.24 | 584141.55 |

10 | 584141.55 | 23365.66 | 41637.67 | 18272.01 | 565869.54 |

11 | 565869.54 | 22634.78 | 41637.67 | 19002.89 | 546866.65 |

12 | 546866.65 | 21874.67 | 41637.67 | 19763.01 | 527103.65 |

13 | 527103.65 | 21084.15 | 41637.67 | 20553.53 | 506550.12 |

14 | 506550.12 | 20262 | 41637.67 | 21375.67 | 485174.46 |

15 | 485174.46 | 19406.98 | 41637.67 | 22230.69 | 462943.76 |

16 | 462943.76 | 18517.75 | 41637.67 | 23119.92 | 439823.84 |

17 | 439823.84 | 17592.95 | 41637.67 | 24044.72 | 415779.12 |

18 | 415779.12 | 16631.16 | 41637.67 | 25006.51 | 390772.62 |

19 | 390772.62 | 15630.9 | 41637.67 | 26006.77 | 364765.85 |

20 | 364765.85 | 14590.63 | 41637.67 | 27047.04 | 337718.81 |

21 | 337718.81 | 13508.75 | 41637.67 | 28128.92 | 309589.89 |

22 | 309589.89 | 12383.6 | 41637.67 | 29254.08 | 280335.82 |

23 | 280335.82 | 11213.43 | 41637.67 | 30424.24 | 249911.58 |

24 | 249911.58 | 9996.463 | 41637.67 | 31641.21 | 218270.37 |

25 | 218270.37 | 8730.815 | 41637.67 | 32906.86 | 185363.52 |

26 | 185363.52 | 7414.541 | 41637.67 | 34223.13 | 151140.38 |

27 | 151140.38 | 6045.615 | 41637.67 | 35592.06 | 115548.33 |

28 | 115548.33 | 4621.933 | 41637.67 | 37015.74 | 78532.59 |

29 | 78532.59 | 3141.304 | 41637.67 | 38496.37 | 40036.22 |

30 | 40036.22 | 1601.449 | 41637.67 | 40036.22 | 0.00 |

**d.** If Billy takes out a 20-year, $720,000
mortgage at 3.5%, his mortgage payments will be,

=PMT(3.5%,20,720000,0,0) = **$50659.98**

Year |
Opening Loan |
Interest @ 3.5% |
Installment |
Principal Repayment |
Closing |

1 | 720000 | 25200 | 50659.98 | 25459.98 | 694540.02 |

2 | 694540.02 | 24308.9 | 50659.98 | 26351.07 | 668188.95 |

3 | 668188.95 | 23386.61 | 50659.98 | 27273.36 | 640915.59 |

4 | 640915.59 | 22432.05 | 50659.98 | 28227.93 | 612687.66 |

5 | 612687.66 | 21444.07 | 50659.98 | 29215.91 | 583471.75 |

6 | 583471.75 | 20421.51 | 50659.98 | 30238.46 | 553233.29 |

7 | 553233.29 | 19363.17 | 50659.98 | 31296.81 | 521936.48 |

8 | 521936.48 | 18267.78 | 50659.98 | 32392.20 | 489544.28 |

9 | 489544.28 | 17134.05 | 50659.98 | 33525.93 | 456018.35 |

10 | 456018.35 | 15960.64 | 50659.98 | 34699.33 | 421319.02 |

11 | 421319.02 | 14746.17 | 50659.98 | 35913.81 | 385405.21 |

12 | 385405.21 | 13489.18 | 50659.98 | 37170.79 | 348234.42 |

13 | 348234.42 | 12188.2 | 50659.98 | 38471.77 | 309762.65 |

14 | 309762.65 | 10841.69 | 50659.98 | 39818.28 | 269944.36 |

15 | 269944.36 | 9448.053 | 50659.98 | 41211.92 | 228732.44 |

16 | 228732.44 | 8005.635 | 50659.98 | 42654.34 | 186078.10 |

17 | 186078.10 | 6512.734 | 50659.98 | 44147.24 | 141930.86 |

18 | 141930.86 | 4967.58 | 50659.98 | 45692.40 | 96238.47 |

19 | 96238.47 | 3368.346 | 50659.98 | 47291.63 | 48946.84 |

20 | 48946.84 | 1713.139 | 50659.98 | 48946.84 | 0.00 |

**e. ** Billy will save
**$235930.64,** if he took out a 20-year mortgage
versus a 30-year mortgage.

Total Interest @ 4% | $5,29,130.14 |

Total Interest @ 3.5% | $2,93,199.51 |

Total Savings |
$2,35,930.64 |

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