Wake Up and Smell the Coffee!
Question 1. Based on the information provided, if the Halls continue making minimum payments on their outstanding debts, how much money will they have left over for all other expenses?
Answer:
To determine how much money will they have left over for all other expenses, we have to compute first the total annual income of Halls minus the annual tax rate and outstanding debts, thus we have:
Total Annual Salary of Halls= $900,000 @ 28% tax rate = $648,000
Debts:
Credit Cards: $10,000 @ 15.99% = $11,599 annually
College Loans: $12,000 @ 5.25% = $18,300 annually
Car Loans: $ 5,000 @ 5.99% = $5,299.50 annually
Then the total left over excluding the house rent and other expenses is:
Left over= $648,000 – ($11,599 + $18,300 + $5,299.50)
= $612,801.50
Question 2. How much money will Laura and Marty have to deposit each month (beginning one month after the child is born and ending on his or her 18th birthday) in order to have enough saved up for their child’s college education. Assume that the yield on investments is 8% per year, college expenses increase at the rate of 4% per year, and that their child will enter college when he or she turns 18 and will complete the degree in 4 years.
Answer:
To complete this task, the Halls need to determine first the amount of college expenses at the 18th, 19th, 20th, and 21st age of their son/daughter which is relatively increasing at 4% per year. After combining the sum of these 4 college expenses at the 18th, 19th, 20th, and 21st age of their son/daughter, Marty and Laura can now determine the amount of money needed each month in order to reach the total expenses of college education of their son/daughter using the sinking fund formula ( 1995).
To find the amount of college expenses at the 18th, 19th, 20th, and 21st age of their son/daughter, we have to use the compound interest formula at i=.04, n=18,19, 20 and 21, and P=$20,000. Then we have
Expenses at:
18th age of their son/daughter=
19th age of their son/daughter=
20th age of their son/daughter=
21st age of their son/daughter=
Then the possible expenses for college education of son/daughter of Laura and Marty is
+ + + = $172,051.13
For the amount of money needed each month in order to reach the total expenses of college education of their son/daughter, the use of sinking fund formula was applied (Jaffe, A. J. and Sirmans, C. F. 1995). Then we have:
Where: S= amount needed to be accumulated
R= amount of deposits per period of payment
i=interest
N= number of payments
Actually, if an individual sees the need to have a certain sum at some future date for the purpose of paying an obligation in lump sum, he/she has to accumulate a fund making periodic deposits. In this case, we have S= $172,051.13, i = 0.08, n=18 for 18 years and R=?, then we have,
And since stands for annual payment, then we have to divide it by 12 to get the monthly deposits of Halls i.e.
Question 3. How much money will the Halls have to set aside each month so as to have enough saved up for a down payment on $140,000 house within 12 months? Assume that the closing costs amount 2% of the loan and that the down payment is 10% of the price.
Answer:
To answer this, the use of amortization formula was applied considering that the down payment on $140,000 house is 10% i.e. $14,000 with closing costs amount 2% of the loan at 12 months. Then we have,
Question 4. If the interest rate on a 30-year mortgage is at 5% per year when the Halls purchase their $140,000 house, how much will their mortgage payment be? Ignore insurance and taxes.
Answer:
To find the mortgage payment, we have to use the amortization formula i.e.
Thus the annual mortgage payment is .
Question 5. Construct an amortization schedule for the 5%, 30-year mortgage.
Answer:
Period
Balance
Installment
Interest
Payment
1
140000
9107.2
7000
2107.2
2
137892.8
9107.2
6894.64
2212.56
3
135680.24
9107.2
6784.012
2323.188
4
133357.052
9107.2
6667.8526
2439.347
5
130917.7046
9107.2
6545.88523
2561.315
6
128356.3898
9107.2
6417.819492
2689.381
7
125667.0093
9107.2
6283.350466
2823.85
8
122843.1598
9107.2
6142.157989
2965.042
9
119878.1178
9107.2
5993.905889
3113.294
10
116764.8237
9107.2
5838.241183
3268.959
11
113495.8648
9107.2
5674.793242
3432.407
12
110063.4581
9107.2
5503.172905
3604.027
13
106459.431
9107.2
5322.97155
3784.228
14
102675.2025
9107.2
5133.760127
3973.44
15
98701.76267
9107.2
4935.088134
4172.112
16
94529.65081
9107.2
4726.48254
4380.717
17
90148.93335
9107.2
4507.446667
4599.753
18
85549.18001
9107.2
4277.459001
4829.741
19
80719.43902
9107.2
4035.971951
5071.228
20
75648.21097
9107.2
3782.410548
5324.789
21
70323.42151
9107.2
3516.171076
5591.029
22
64732.39259
9107.2
3236.61963
5870.58
23
58861.81222
9107.2
2943.090611
6164.109
24
52697.70283
9107.2
2634.885142
6472.315
25
46225.38797
9107.2
2311.269399
6795.931
26
39429.45737
9107.2
1971.472869
7135.727
27
32293.73024
9107.2
1614.686512
7492.513
28
24801.21675
9107.2
1240.060838
7867.139
29
16934.07759
9107.2
846.7038794
8260.496
30
8673.581468
9107.2
433.6790734
8673.521
Total
273216
133216.0605
139999.9
Question 6. If the Halls want to have an after-tax income when they retire as they currently have, and assuming they live until they are 80 years old, how much money should they set aside each month so as to have enough money accumulated in their retirement nest egg? Assume that annual inflation rate is 4% per year for the whole term, and the investment return is 8% per year before and after retirement, and that their tax rate is 28% through out their life.
Answer:
As stated the total life span of Marty and Laura is only up to 80 years thus they only have 45 years of life since they are both 35 years old. Referring to the computation in Question 1, the total annual salary of Halls is $648,000 with 28% tax. And since they wanted an after-tax income when they retire as they currently have, then we have to determine the total amount value they needed in their 66-80 years old with 4% inflation rate. Using the compound interest formula illustrated by Hertz, D. B. (1964) in his paper we have,
Amount needed at their age of 66 years old is
=$2067061.214
Amount needed at their age of 67 years old is
=$2149743.662
Amount needed at their age of 68 years old is
=$2235733.409
Amount needed at their age of 69 years old is
=$2325162.745
Amount needed at their age of 70 years old is
=$2418169.255
Amount needed at their age of 71 years old is
=$2514896.025
Amount needed at their age of 72 years old is
=$2615491.866
Amount needed at their age of 73 years old is
=$2720111.541
Amount needed at their age of 74 years old is
=$2828916.002
Amount needed at their age of 75 years old is
=$2942072.642
Amount needed at their age of 76 years old is
=$3059755.548
Amount needed at their age of 77 years old is
=$3182145.77
Amount needed at their age of 78 years old is
=$3309431.601
Amount needed at their age of 79 years old is
=$3441808.865
Amount needed at their age of 80 years old is
=$3579481.219
And summing up the amounts in these 15 periods, we obtain $41,389,981.36. Meaning to say, Laura and Marty need to have $41,389,981.36. after their retirement. Now, to determine the amount of money should they set aside each month so as to have enough money accumulated in their retirement nest egg, we will use the sinking fund formula with S= $41,389,981.36, i= 0.08 and n=30 years before retirement. Then we have,
And since stands for annual payment for their retirement benefits, then we have to divide it by 12 to get the monthly deposits of Halls i.e.
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