Question

1. You are trying to determine how much you need in order to retire comfortably. You would like a monthly retirement income of $20,000 and anticipate living for 30 years in retirement. The first retirement check will come at the end of your first month of retirement. You have already saved $40,000. You expect to earn 6% on your investments. You have 40 years until you retire. How much must you save at the end of each month between now and the day you retire, with your first savings deposit in one month, in order to fund your retirement?                                 

a.           $1,212.46                                                    

b.           $1,454.96                                                                                              

c.           $4,437.30                                                                                               

d.           $1,745.95                                                                                               

e.           $3,395.30

I know the answer is in bold, but i do not know how to get here with a BA ii plus

Answer 1

We need to break this question into 2 parts:

1. We need to calculate the PV (at start of retirement) of the monthly annuity of $20,000 for 30 years, with 6% rate of interest.

PV =?, when FV = 0, N = 30 * 12 = 360, I/Y = 6%/12 = 0.50%, PMT = 20000

Steps for calculator are:

a. It is always a good practice to clear your calculator memory before you start calculating. Clear TVM worksheet. Press "2^nd”  [CLR TVM] “2^nd”  [QUIT]

b. Now input all the variables. Enter 0 and Press [FV]. Enter 360 and Press [N]. Enter 0.5 and Press [I/Y]. Enter 20000 and Press [PMT].

c. Now calculate PV. Press [CPT] then Press [PV]. PV = 3,335,832.29

You are done with the first part. Let us move to second.

2. We need to calculate the value of annuity (or the amount that we need to save every month, starting next month) to reach the PVcalculated in part 1, which is future value here. Remember, I was prudent enough to save $40,000 already which is my PV. Time period is 40 Years.

PMT =?, when FV = 3,335,832.29, N = 40 * 12 = 480, I/Y = 6%/12 = 0.50%, PV = -40000 (PV and PMT will both bear negative signs as they are inflows, and FV will be hence of opposite polarity, since it is an outflow)

Steps for calculator are:

a. As mentioned earlier, it is always a good practice to clear your calculator memory before you start calculating. Clear TVM worksheet. Press "2^nd”  [CLR TVM] “2^nd”  [QUIT]

b. Now input all the variables. Enter 3,335,832.29 and Press [FV]. Enter 480 and Press [N]. Enter 0.5 and Press [I/Y]. Enter -40000 and Press [PV].

c. Now calculate PMT. Press [CPT] then Press [PMT]. PMT = - $1,454.96

Negative Sign indicate that you would need to deposit the amount (an outflow from your cash balance).