Question

Shelli graduates from the University of South next month on her 25^th birthday, and she is excited to begin her new career. Because she wants to have a comfortable living when she retires, Shelli has decided to begin planning for her retirement now. As a result, she is currently evaluating the amount she needs to contribute to a retirement fund satisfy her financial requirements at retirement. After speaking to retired friends and relatives, Shelli estimates she will need $60,000 each year to be able to live comfortably and enjoy her “twilight years.” In addition, Shelli expects that she can invest in a retirement fund that will yield 8 percent interest compounded annually for a long as she contributes to the fund. As soon as she retires, Shelli will have to move her retirement “nest egg” to another investment so she can withdraw money when she needs it. Her plans are to move the money to a fund that allows withdrawals at the beginning of each year and pays 5 percent interest compounded annually. Shelli expects to retire in 40 years, and, after taking an online “life expectancy” quiz, she has concluded that she will live another 25 years after she retires. If Shelli’s expectations are correct, how much must she contribute to the retirement fund to satisfy her retirement plans if she intends to make her first contribution to the fund one year from today and the last contribution on the day she retires?

Alvin wants to save money to pay for his college education, which he plans to start in three years. Currently, the cost per year (for everything—food, clothing, tuition, books, transportation, and so forth) to attend the college he has chosen is $15,000; but these costs are expected to increase at the same rate as inflation, which is 3 percent, each year. Alvin plans to make three equal annual deposits into his “education” investment account beginning today. These deposits will earn 8 percent interest.

a.   If he plans to finish his college degree in four years, what will be the cost of Alvin’s education each year he is in college?

b.   How much must Alvin contribute each year so that he has enough money in his education fund when he starts college in three years to pay the costs for the four years it takes him to complete his degree?

Answer 1

Shelli

A be the sum of present value of amount withdrawn each year after retirement

interest rate = 5% = 0.05

A = 968464.41

Let x be the annual amount she saves each year starting 1 year from now

F be the sum of all the future values of such deposits

interest rate = 8% = 0.08

A = F

259.057x = 968464.41

x = $3738.43

She needs to save this much amount each year starting in 1 year for 40 years

Alvin

t=3 means end of 3rd year starting from now

Assuming that the cost of education each year will be incurred at the beginning of each year

The first fee Alvin will have to pay will be at t=3 (ie end of 3 years or beginning of 4th year)

(a)

Year	Cost of education (adjusted for inflation)
t=3	15000*(1+3%)^3 = 16390.9
t=4	15000*(1+3%)^4 = 16882.63
t=5	15000*(1+3%)^5 = 17389.11
t=6	15000*(1+3%)^6 = 17910.78

(b)

Let x be the deposit amount made at t=0,1&2 respectively

deposit rate = 8% = 0.08

Present value of deposit = PV

Present value of education cost = PV

PV = 48542.44

2.783x = 48542.44

x = $17440.83 (deposit to be made each year)