Question

Question 1

After graduation, you plan to work for Donald’s Fashion Co. for 7 years and then start your own business. You expect to save and deposit $ 10,000 a year for the first 3 years (t = 1 through t = 3) and $14,000 annually for the next 4 years (t = 4 through t = 7). The first deposit will be made a year from today. In addition, your grandfather just gave you a $40,000 graduation gift which you will deposit immediately (t = 0). If the account earns 8% compounded annually, how much will you have when you start your business 7 years from now?

Question 2

Your sister turned 20 today, and she is planning to save $5,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that's expected to provide a return of 7% per year. She plans to retire 40 years from today, when she turns 60, and she expects to live for 25 years after retirement, to age 85. Under these assumptions, how much can she spend each year after she retires, if she can earn 9 % per year after retirement. Her first withdrawal will be made at the endof her first retirement year.

Question 3

After working for a long time (20 years) with your company, you have decided to accept the company’s termination offer of $24,000 per year for 25 years or accept a lump sum of $374,928 one year from today.

1. If you can earn 7% per year on other investments, will you accept this lump sum or take the annuity payments? Show the calculations used to accept or reject any one of the two options.

1. What interest rate the company is offering you in the annuity? Will your decision change?   

  

Question 4 -

4. (a) If you want to be a millionaire in 15 years from now and you can only save $12,000 every which you deposit at the end of every year for 15 years in a mutual fund, what interest rate must you earn to become a millionaire in 15 years? (answer to the closest interest rate)

(b) If you want to be a millionaire in 20 years from now and you can earn 8% interest per year in a mutual fund, how much money must you deposit per year to be a millionaire in 20 years?   

Answer 1

1. Value of first deposit of $40000 after 7 year= 40000*1.08^7=68552.97

Similarly the value of all money after 7 year is $175805.45.Calculation given below:

Year	Deposit	Value of Money after 7th year (i.e. Deposit*1.08^(7-year)
0	40,000.00	68,552.97
1	10,000.00	15,868.74
2	10,000.00	14,693.28
3	10,000.00	13,604.89
4	14,000.00	17,635.97
5	14,000.00	16,329.60
6	14,000.00	15,120.00
7	14,000.00	14,000.00
	Total	175,805.45

2.

Value of deposits at 60 years of age= $204,977.46

Now,

So, she can spend $20867.99 per year

3.

The effective interest given by the company is 4%. Calculation is given below:

1. You should take the lumpsum option over annual payment as you will get more interest rate (7%) rather than company's 4% given interest

2. The interest rate is given 4%, so you will not change your decision.

4.

a)

So, you need to get interest rate of 22% pa

b)

So, you need to deposit 21852.21 per year