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Billy McMahon is interested in buying a waterfront condo and has saved $100,000 for the down...

  1. 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.
    1. 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.
    2. If Billy takes out a 30-year, $720,000 mortgage at 4%, what will his mortgage payments be?
    3. Prepare an amortization schedule to prove that your answer is right and his mortgage will be paid off in 30 years.
    4. If Billy takes out a 20-year, $720,000 mortgage at 3.5%, what will his mortgage payments be?
    5. How much would Billy save if he took out a 20-year mortgage versus a 30-year mortgage?
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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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