What Is a Future Value, and How Is It Calculated? Under the concepts of the time value of money, you can determine the future value of an amount invested today that will earn a given interest rate over a given amount of time. This technique can be used to calculate the future value of (1) a single receipt or payment made or (2) a series of receipts or payments. Dakota and Gabriella are sitting together, with their notebooks and textbooks open, at a coffee shop. They've been reviewing the latest lecture from Dr. Johnson's personal finance class by asking questions of one another. Today's topic addressed the calculation of future values for both simple and compound interest-earning accounts. DAKOTA: So, why is it important to be able to calculate the future value of some amount invested? GABRIELLA: First, remember that the amount invested is usually called , and the amount earned during the investment period is called . It is important to be able to calculate a future value so that you can know in advance what a given amount of principal will be worth after earning a specified for a known DAKOTA: OK, I understand that and I know the amount invested today can be called the value of the investment, whereas the amount realized after the passage of " t " period of time is called its value. But what causes the present and future values to be different values? GABRIELLA: Two things cause the present and future values to be different amounts. First, the earned during the investment period causes the future value to be greater than, equal to, or less than the present value. Second, the method used to calculate the interest earned-that is, whether the account pays interest-determines the amount by which the future value differs from the present value. DAKOTA: That makes sense and I remember Dr. Johnson says that the difference between simple and compound interest is that in the case of interest, interest is earned solely on the invested principal, but in the case of interest, interest is earned on not only the principal but also previously earned interest. GABRIELLA: Very good! So, here's your next question. Assuming equal amounts of principal, interest rates, and investment periods, which type of account should produce the greater future value: the account earning simple interest or the account earning compound interest? DAKOTA: By my reasoning, the account earning interest should have the greater future value, assuming the identical amounts of principal, interest rates, and investment periods. GABRIELLA: Again, correct! But now, I want you to prove it. So, let's assume that you invest $2,000 into two different accounts, both of which earn 7% per year, and the money is invested for three years. Account A earns simple interest, while account X earns compound interest. By how much will the future value of account X exceeds the future value of account A ? Here is a sheet of paper, show me how to calculate the future values of the two accounts. DAKOTA: OK, let me see what I can do ... Future Value of Account A Note: Account A pays simple interest. Round your answer to two decimal places. =Principal+[(PrincipalInterestRate)InvestmentPeriod]=$2,000+[($2,0007%)3years]= Future Value of Account X Note: Account X pays compound interest. Round your answer to two decimal places. Future Value xX= Present Value Interest Rate Factor =PresentValue(1+InterestRate)nyears=$2,000(1+0.07)3= To find the interest rate factor, you can use three different ways, including multiplying it out: Interest Factor =(1+0.07)(1+0.07)(1+0.07)=1.2250 Or using exponents and calculating it directly: Interest Factor =(1+0.07)3=1.2250 Or looking up the value in the Future Value Interest Factor Table: The fourth alternative for solving the equations is to let a financial calculator perform the calculation. This requires that you know how your calculator functions and how to enter the following variables: P/Y indicates the number of compounding periods per year, N is the number of years, I is the interest rate, PV is present value, and FV is future value. Difference in Future Values Note: Round your answer to two decimal places. The fourth alternative for solving the equations is to let a financial calculator perform the calculation. This requires that you know how your calculator functions and how to enter the following variables: P/Y indicates the number of compounding periods per year, N is the number of years, I is the interest rate, PV is present value, and FV is future value. Difference in Future Values Note: Round your answer to two decimal places. Difference=FVXFVA= DAKOTA: So, what do you think? GABRIELLA: Your work looks fantastic! But now I've got to challenge you with one last question: What would happen to the two future value numbers and the difference between them if the two accounts did not pay interest? DAKOTA: Uh ... if the interest rate were zero, then interest would ; the future value of account A would be ; the future value of account X would be and the difference between the two accounts would be GABRIELLA: Correct! You are so ready for Dr. Johnson's next quiz