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= 0,000 @ 28% tax rate = 8,000


Debts:


            Credit Cards: ,000 @ 15.99% = ,599 annually


            College Loans: ,000 @ 5.25% = ,300 annually


            Car Loans: $ 5,000 @ 5.99% = ,299.50 annually


 


Then the total left over excluding the house rent and other expenses is:


Left over= 8,000 – (,599 + ,300 + ,299.50)


               = 2,801.50


 


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=,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


+ + + = 2,051.13


 


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= 2,051.13, 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 0,000 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 0,000 house is 10% i.e. ,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 0,000 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 8,000 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


=67061.214


Amount needed at their age of 67 years old is


=49743.662


Amount needed at their age of 68 years old is


=35733.409


Amount needed at their age of 69 years old is


=25162.745


Amount needed at their age of 70 years old is


=18169.255


Amount needed at their age of 71 years old is


=14896.025


Amount needed at their age of 72 years old is


=15491.866


Amount needed at their age of 73 years old is


=20111.541


Amount needed at their age of 74 years old is


=28916.002


Amount needed at their age of 75 years old is


=42072.642


Amount needed at their age of 76 years old is


=59755.548


Amount needed at their age of 77 years old is


=82145.77


Amount needed at their age of 78 years old is


=09431.601


Amount needed at their age of 79 years old is


=41808.865


Amount needed at their age of 80 years old is


=79481.219


 


            And summing up the amounts in these 15 periods, we obtain ,389,981.36.  Meaning to say, Laura and Marty need to have ,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= ,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.


 



Credit:ivythesis.typepad.com



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