During your lifetime, you’ll want your money working for you. A good start is understanding calculations you can use to plan and track your financial progress. The principle of compound growth is a powerful concept that can begin putting your money to work for you. By knowing how to calculate interest, you’ll quickly see the benefit of saving and investing, and understand the cost of borrowing money. When you’re through with this tutorial, you’ll be able to answer questions like:
Once you have defined your financial goals, you need to link each hoped-for outcome with your current financial information. This is where financial tools come into play. Time value of money (TVM) formulas and calculations are valuable personal finance tools because they allow you to specifically consider financial goals in terms of money, time, and interest.
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Anytime you are working with a financial goal that involves money, time, and interest, you will want to use TVM calculations. For some students, TVM is a challenging aspect of learning about personal finance topics. This is, after all, the one area that requires the use of math formulas and calculations. But remember—especially if you have a math phobia—that doing these TVM calculations becomes much easier with a little practice.
Most individuals also prefer to use a financial calculator, app, or computer spreadsheet program to solve TVM problems. Financial calculators or TVM apps are easy to use and simplify the math. We will include some basic instructions for using a calculator to solve TVM problems in another topic.
Let’s start with a basic outline of four common types of TVM problems. These are the tools that you’ll use to measure your financial goals:
IN CONTEXT
- PV = $1,000: You know what you have today ($1,000). This is called the present value (PV).
- I = 10%: you know the rate of return (I) of what you can earn on your money each year (10%).
- N = 3: you know the number of periods (N) in which you will earn your return (3 years).
- FV = ?: you are trying to find the future value (FV), which is what you will have at the end of the 3-year period.
We’ll show you in another topic how you can use a TVM formula, calculator, or table to determine the future value of a lump sum. But for now, you can get this answer by multiplying $1,000 by (1.10 × 1.10 × 1.10), which equals $1,331. Notice that when you are looking for a future value, you multiply your present value by a factor greater than 1.0.
..IN CONTEXT
- For example, how much do you need today (PV) if you know that you will need $5,000 (FV) in 3 years (N) assuming you can earn 10% interest (I)?
- With these inputs and working backward, you can determine that you need $3,757 in hand today (PV) to reach your goal.
- This process of determining the present value is called discounting the future value.
We’ll show you in another topic how to use a TVM formula to determine the present value of a lump sum, but for now you can get this answer by multiplying $1,000 by ([1/1.10] × [1/1.10] × [1/1.10]) or $1,000 by (0.9091 × 0.9091 × 0.9091). Notice that when finding the present value, you multiply the future amount by a factor that is less than 1.0.
IN CONTEXT
- For example, assume you are investing $2,000 (PMT) at the end of each year for 3 years (N) at a rate of return (I) of 10%. The present value (PV) is $0, which means that there is no other money in the account at the start.
- With these inputs, at the end of the compounding period, you’ll have a future value (FV) of $6,620.
We’ll show you in another topic how to use a TVM formula to determine the future value of an annuity, but for now you can get this answer by using the following calculation (each period is represented in brackets): [2,000] + [1.1] + [1.1].
.When calculating the payment needed to pay off a loan (PMT), you need to know the number of payments (N), the interest being paid (I), and the starting loan amount (PV).
IN CONTEXT
Say you want to purchase a car with a loan. How would you calculate the amortization schedule using TVM?
- The amortization calculation will tell you how much you need to pay per month to pay off the loan.
- To do this calculation correctly, you must be specific when choosing the number of payments. For example, most home, automobile, and student loans are amortized on a monthly basis. This means that if you have a 5-year loan, you’ll actually be making 60 payments.
- The interest input needs to be adjusted. If your loan APR is 6%, then you are really paying 0.50% (6% ÷ 12) per month in interest.
The math for this calculation is a bit more involved, but we’ll show you a shortcut for doing a payment calculation next.
EXAMPLE
Let’s say you want to estimate how many years it will take your money to grow from $3,000 to $6,000 if you can earn 3% interest.EXAMPLE
Now let’s say you want to know what interest rate you need to earn to turn $3,000 into $6,000 over 6 years.As shown in the table below, the Rule of 72 works nicely as a way to approximate how long it will take to double your money for any financial goal. The higher the interest rate, within reason, the more accurate the Rule of 72 becomes. In situations in which the interest rate is very low—say, below 5%—then you might want to substitute 70 for 72.
Rate | Actual Periods | Rule of 72 Estimate | Rule of 70 Estimate |
---|---|---|---|
1.00% | 69.66 | 72.00 | 70.00 |
2.00% | 35.00 | 36.00 | 35.00 |
3.00% | 23.45 | 24.00 | 23.33 |
4.00% | 17.67 | 18.00 | 17.50 |
5.00% | 14.21 | 14.40 | 14.00 |
6.00% | 11.90 | 12.00 | 11.67 |
7.00% | 10.24 | 10.29 | 10.00 |
8.00% | 9.01 | 9.00 | 8.75 |
9.00% | 8.04 | 8.00 | 7.78 |
10.00% | 7.27 | 7.20 | 7.00 |
11.00% | 6.64 | 6.55 | 6.36 |
12.00% | 6.12 | 6.00 | 5.83 |
13.00% | 5.67 | 5.54 | 5.38 |
14.00% | 5.29 | 5.14 | 5.00 |
15.00% | 4.96 | 4.80 | 4.67 |
IN CONTEXT
Jared is saving for a down payment to purchase a house. Based on his budget, he can save $4,500 per year while earning a 5% rate of return (APY). How much will Jared have for a down payment at the end of 5 years? Use the mathematical processes demonstrated in this topic, or you can use an online TVM calculator or app, to determine the answer.
The inputs are PV ($4,500), N (5 years), and I (5%). The answer (output, or FV) is $24,865.34. You can estimate this amount by using the following calculation (each period is represented in brackets): [4,500] + [1.05] + [1.05] + [1.05] + [1.05].
Source: THIS WORK IS ADAPTED FROM CHAPTER 2.2 OF JOHN WILEY & SONS, INC. EBOOK, “INTRODUCTION TO PERSONAL FINANCE: BEGINNING YOUR FINANCIAL JOURNEY” BY JOHN E. GRABLE PHD, CFP AND LANCE PALMER PHD, CPA, CFP.