Case Scenario:
How much do you think you will need to retire comfortably at age 60? Would you believe that you’re going to need at least $4,000,000? Assuming you’re 18-25 years old (or younger), it’s true! Sounds hard to believe, but by the end of this discussion, you should be a believer. The first thing you need to do is define “comfortably”. Everyone is going to have their own
definition of that, but we are going to assume that your house is paid off and that you would want $50,000 of income each year. Some of you will want more, but we’re going to use that number as a starting point. Don’t forget, at that age, you’re going to want to go on trips, see your grand kids, etc. and will have lots of medical bills! I’m also demonstrating absolutely no confidence in our government to have Social Security still hanging around by the time you and I retire! So if it’s still around when we retire, then it’s just a nice added bonus. However, the average person today only receives about $1000 per month for Social Security. Is that enough to live on for retirement? No! Not even close. But like I already said, I don’t think it will still be around by the time we retire.
A big mistake in planning retirements is forgetting inflation. Remember, prices go up almost every year. Inflation has averaged about 4.5% during the last generation or so. It has been a lot lower than that just recently, and much higher than that a lot earlier, but we are going to use an average. (This number will vary depending on what years you look at, but we will use 4.5% for this discussion.) That doesn’t sound like much, but it is. For example, if you are age 18-22 years old, by the time you are age 60, it will cost you
almost $250,000 to buy what it cost you to buy $50,000 today! In other words, if I gave you $50,000 and you went out and bought groceries, gas, a car, whatever, and then you went out and bought the same things at age 60,
it would cost you about $250,000 to buy what costs you $50,000 today! But wait, it gets worse! At age 90 it’s going to cost you about $900,000 to buy what $50,000 will buy today! Yikes!!
But why take my word for it when you can calculate this Yourself. There is the compound interest formula, A = P(1 + r) ^ t , where the “ ^ “ (carrot) symbol means “to the power of”. Here A is the amount of money we have after investing P amount of money at interest rate r for t years. We can also use this formula to calculate the increasing costs of inflation. Let P = 50,000, r = .045 (4.5% converts to .045 by moving the decimal place two places to the left), and let t = 37 (assuming you’re about 23 years old, you’ll be 60 in 60 - 23 = 37 years). Plug that into your TI-83 and see what you get. Be sure to take (1 +.045) to the power of 37 BEFORE you multiply it times 50,000! You should get around $250,000. Now for the Unit 1 Discussion, REPLY to this discussion by answering (or stating the results of) the following 5 problems/questions:
1. If you went out and bought $50,000 worth of things today, how much would it cost you to buy approximately the same things at age 60? (Use page 25 with Let P = 50,000, r = .045 (4.5%), and let t = the number of years until you are 60. So if you are 20 years old, the let t = 60 – 20 = 40). Is this number what you expected? Much higher/lower? Much scarier?
Do get you started, your formula should look something
Like this:
A = 50000(1 + .045)^(37)
Again, the ^ symbol means “to the power of”.
2. Do the same thing for problem #1, except let t = the number of years until you are age 90. So if you are 31, then n = 60 – 31 = 29. Does that number surprise you? Is that depressing or what!?
3. Now make a table with two columns. One column labeled “Age” and the other column labeled “Amount Needed”. The second column is going to be the amount you need for retirement, corresponding to your age that year. So, your first entry for the “Age” column will be 60, and next to that will be your first entry for “Amount Needed”, which will be your answer for the first question (above). Now number the age column 61, 62, etc all the way down to 90. Then using your TI-83, calculate the amount you will need every year up to age 90. This sounds like a lot of work, but what you can do is enter the numbers for question #1 (Let P = 50,000, i = .045 (4.5%), and let t = the number of years until you are 60) and then hit enter on your TI-83. Then hit the yellow “2nd” key followed by the key where above it you see “Entry”. You should see the same thing you just typed in earlier. Now go in and change the t value corresponding to you being age 61 and hit enter.
Continue this procedure all the way down until age 90. KEEP THIS VERY DEPRESSING TABLE, AS WE WILL BE USING IT IN LATER DISCUSSIONS! I recommend typing it in a word or excel file and saving it! What do you see happening? That “little” 4.5% makes a big difference when you take 4.5% of big number doesn’t it!? Just to get you started, IF you are 25 years old, then your calculations and table would look like this (if you’re an age different than age 25, then your numbers will of course be different):
P = 50000
i = .045
t = 60 – 25 = 35
At age 60, amount needed would be:
A = 50000(1.045)^35 = $233,367
At age 61, t = 61 – 25 = 36
So at age 61, amount need would be:
A = 50000(1.045)^36 = $243,869
So you’re the start of your table would look like this:
Age Amount Needed
60 233,367
61 243,869
And then you would want to complete this table until age 90.
4. Total up all the numbers in the “Amount needed” column. Wow! That’s some serious money! How do you feel about that? Don’t worry, we are going to use Algebra to figure out a way to come up with that much money!
5. Now do you believe that you need at least $4,000,000 to retire at age 60?
Stay tuned for the next discussion as we start to dive deeper into how to come up with this outrageous amount of money so we can retire!
Provide complete and step by step solution for the question and show calculations and use formulas.