Question

1.  You are saving for retirement. You have decided that one year from today you will begin investing 10 percent of your annual salary in a mutual fund which is expected to earn a return of 12 percent per year (compounded semi-annually). Your present salary is $30,000, and you expect that it will grow by 4 percent per year throughout your career (consequently, your investment at time 1 will be $3,000, your investment at time 2 will be $3,120, etc.). You will retire 40 years from today.

a)  How much money will you have in your investment account at retirement (assume you make your last investment deposit 40 years from now on the day you retire)?

b)  At retirement, you shift your investment portfolio balance into a money market account earning 6% per year, compounded monthly. You would like to make an equal monthly withdrawal from this money market account over the next 20 years (first withdrawal beginning one month into retirement at time 40 + one month). What equal, monthly amount can you withdraw from the account so that at time 60 (20 years into retirement) your money market account balance is reduced to $0?

Answer 1

FV of annuity
P = PMT x (((1 + r)^n-(1+g)^n)/(r-g))
Where:
P = the future value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
Annual Payment starting	3000
Growth rate	4%
Interest	12%
compounding	semi-annual
Effective interest rate	((1+12%/2)^2)-1)
Effective interest rate	12.360%
Total corpus accumulated=	P = PMT x (((1 + r)^n-(1+g)^n)/(r-g))
Total corpus accumulated=	3000* (((1 + 12.36%)^40-(1+4%)^40)/(12.36%-4%))
Total corpus accumulated=	3,624,221.51
PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
Interest	6%
compounding	Monthly
Effective interest rate	((1+6%/12)^12)-1)
Effective interest rate	6.16778%
3,624,221.51	P = PMT x (((1-(1 + r) ^- n)) / i)
3624221.514	=PMT *(((1-(1 + 6.1677%) ^- 20)) / 6%)
3624221.514	=Annual Payment * 11.631
Annual withdrawal=	=3624221.51/11.631
Annual withdrawal=	311,600.16
Monthly withdrawal=	25,966.68