Time Value of Money
Although Time Value of Money (TVM) looks very intimidating at first glance, it is actually quite simple and interesting. By manipulating the variables in the TVM equation, TVM can essentially tell you how much any amount of money will be worth at any point in time. This can be an excellent tool for personal finance, especially when you want to know how much your money will be worth in the future. Want to be a millionaire? TVM will show you how to make it a reality.
SOLVING BASIC TVM EQUATIONS BY HAND
PV = FV/[(1+i)^n]
FV = PV*[(1+i)^n]
PV: present value at time = 0
FV: future value at time = n
i: rate of compounding per period
n: number of periods
SOLVING BASIC TVM EQUATIONS USING TI83+ CALCULATOR
Step 1. Press APPS
Step 2: Select #1: Finance
Step 3: Select #1: TVM Solver
Now your calculator screen should look like this:
N=0 … N represents the number of periods
I%=0 … I% represents the rate of compounding per period as a percentage
PV=0 … PV represents the present value at time = 0
PMT=0 … PMT represents the payment amount per period
FV=0 … FV represents the future value at time = n
P/Y=1
C/Y=1
PMT:END
Step 4: Enter all information given for the variables N, I%, PV, PMT, FV.
Step 5: Press the ALPHA button then ENTER to solve for the missing variable.
* Important Notes: The formula the calculator uses requires that one of the three (PV, PMT, or FV) must be negative even if all three represent positive values. Because our focus is understanding the basics of TVM, P/Y and C/Y will remain equal to 1 and PMT will remain on END not BEGIN. Therefore, we will not include them in the examples below. For the sake of space, we will flip the calculator screen from vertical to horizontal for our examples.
SAMPLE TVM PROBLEMS USING TI83+ CALCULATOR
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Question: I am 25 years old today and have no money invested. Assuming 7% annual return on my investments, how much money will I have to invest each year to retire at age 65 with $1,000,000? (What if I am 35? 45?)
N=65-25=40 I%=7 PV=0 PMT=? FV=1,000,000
Solve for PMT. PMT=5,009.14
Answer: Assuming 7% interest, $5,009.14 invested each year would be worth $1,000,000 in 30 years. ($10,586.40, $24,392.93). It is important to notice how much more would have to be invested each year if you start when you are age 35 or age 45 as opposed to age 25. The later you begin investing, the more you will have to invest each year in order to catch up.
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Question: If I am 25 years old today and want to retire at age 65 with $1,000,000, how much will if have to invest today assuming my investments make a 7% annual return? (What if I am 35? 45?)
N=65-25=40 I%=7 PV=? PMT=0 FV=1,000,000
Solve for PV. PV=66,780.38
Answer: Assuming 7% interest, $66,780.38 invested today would be worth $1,000,000 in 40 years. ($131,367.12, $258,419.00). It is important to notice how much more would have to be invested if you start when you are age 35 or age 45 as opposed to age 25. The later you begin investing, the more you will have to invest in order to catch up.
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Question: Assuming I intend to invest $5,000 each year for 30 years, what will the difference be in the future value of money if I am earning 4%, 7%, or 10% interest annually on my money?
N=30 I%=4 PV=0 PMT=5,000 FV=?
Solve for FV. FV=280,424.69
N=30 I%=7 PV=0 PMT=5,000 FV=?
Solve for FV. FV=472,303.93
N=30 I%=10 PV=0 PMT=5,000 FV=?
Solve for FV. FV=822,470.11
Answer: Investing $5,000 each year for 30 years will be worth $280,424.69 if it earns 4% interest, $472,303.93 if it earns 7% interest, and $822,470.11 if it earns 10% interest. It is important to notice how much of an effect compound interest has on investment returns. This problem demonstrates that earning 10% interest annually as opposed to 4% interest annually results in almost three time as much money.
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Take time to notice how the manipulation of each of these variables dramatically effects the outcomes. Keep in mind that all of this is directly related to investing. Increasing the length of time you invest (N), increasing the rate of return on your investments (I%), increasing the amount you invest today (PV), and increasing the amount you invest per period (PMT) will each have a significant positive impact on what your money will be worth in the future (FV).