Investment/Retirement

[actang13]

Please help!


After realizing that social security may not exist by the time you retire, you decide it is time to get to work on retirement saving. As an college graduate you will make $45,000 next year before taxes. You expect this salary to grow at 4.5 percent annually until you retire in 40 years. In retirement you believe you will need 65 percent of your final pre-retirement salary to live comfortably. This amount will need to grow at 2 percent annually to keep up with inflation (the first inflation adjustment will occur the year you retire). Due to rising life expectancies, you believe you will need your income in retirement to last 30 years. You will spend your last dollar on the day you die. Funds that you save can be invested in a mutual fund earning 7 percent annually. (Assume all cash flows occur at the end of the year.)

What percent of your salary do you need to invest annually to live comfortably in retirement? (Assume that you invest the same percent every year.)


So far I got the following:

65% of last earning is $162,802.55
Total adjusted first year with inflation for 30 years: $6,736,678.40
Discounted: $2,530,887.98

I know the answer is 15.35% but I'm having difficulty reaching it.

I'm using the solver function in the calculator which is shown as follows:

N= 40
I%= 7
PV= 0
PMT= 0
FV = 2530887.98

And the payment I get is about 4% of my total salary ($4816364.54)

The payment I get is 12677.57

 

[kelride]

My question is, how did you get these figures? I have the same problem in my project for FIN 300 and I can't seem to get the calculations correct, so I'm wondering the steps you took to get these numbers.

 

[tkhunny]

After realizing that social security may not exist by the time you retire, you decide it is time to get to work on retirement saving. As an college graduate you will make $45,000 next year before taxes. You expect this salary to grow at 4.5 percent annually until you retire in 40 years. In retirement you believe you will need 65 percent of your final pre-retirement salary to live comfortably. This amount will need to grow at 2 percent annually to keep up with inflation (the first inflation adjustment will occur the year you retire). Due to rising life expectancies, you believe you will need your income in retirement to last 30 years. You will spend your last dollar on the day you die. Funds that you save can be invested in a mutual fund earning 7 percent annually. (Assume all cash flows occur at the end of the year.)

What percent of your salary do you need to invest annually to live comfortably in retirement? (Assume that you invest the same percent every year.)

You simply MUST learn to manipulate "Basic Principles"

"you will make $45,000 next year before taxes"

\(\displaystyle A = 45000\)

"this salary to grow at 4.5 percent annually"

\(\displaystyle t = 0.045, r = 1+t = 1.045\)

"you retire in 40 years"

\(\displaystyle n = 40\)

"In retirement you believe you will need 65 percent of your final pre-retirement salary to live"

\(\displaystyle B = A*r^{40}*0.65\)

"will need to grow at 2 percent annually to keep up with inflation"

\(\displaystyle q = 0.02, s = 1.02\)

"need your income in retirement to last 30 years"

\(\displaystyle m = 30\)

"invested in a mutual fund earning 7 percent annually"

\(\displaystyle i = 0.07, f = 1.07, v = 1/f = 1/1.07\)

"What percent of your salary do you need to invest annually "

\(\displaystyle p = a*A\) where \(\displaystyle 0 < a < 1\)

Okay, now build it. The guiding principle is that the last deposit gathers no interest. It is deposited at retirement.

\(\displaystyle p*f^{n-1} + p*r*f^{n-2} + p*r^{2}*f^{n-3} + ... + p*r^{n-1} =\) Retirement Funds Required

Now, let's spend it. I presume we can get the same investments during retirement. The guiding principle is that the first payment is one year after retirement. This may seem a little odd, but it is a necessary side effect of the end-of-year assumptions for all cash flows.

Retirement Funds \(\displaystyle = Bv + B*s*v^{2} + B*s^{2}*v^{3} + ... + B*s^{m-1}*v^{m}\)

You should add up those last two expressions. If you cannot do it, you need to practice. Adding a simple geometric series should become second nature to you. Practice, practice!

Slowly, carefully, one piece at a time. I may have defined more variables than I needed. So? More importantly, I defined somethign for everything that was given in the problem. Go deliberately. Do not lose sight of what is asked. The answer to the question is 'a'. Notice how 'a' is NOT in any of my final expressions. You must pay attention.

Basic Principles. Really. They wil save you.