Chapter 25: Future Value of a Single Amount

The future value (FV) of a single amount represents how much a present sum will grow to over time at a given interest rate. This is helpful for understanding investment growth or future liabilities. Calculating FV involves compounding interest over the investment period, which can be simplified using FV tables. Key Concepts 1. Future Value Formula: To find the FV of a single present amount, we adjust the PV formula by multiplying both sides by (1+i)n(1 + i)^n(1+i)n: FV=PV×(1+i)nFV = PV \times (1 + i)^nFV=PV×(1+i)n where: FV = future value (amount in the future) o PV = present value (amount today) o i = interest rate per period o n = number of periods 2. Using Future Value Tables: FV tables provide FV factors for various interest rates and time periods, assuming a present value of 1. To find the FV of amounts other than 1, simply multiply the FV factor by the actual present amount. For example, if i=10%i = 10\%i=10% and n=3n = 3n=3, the FV factor is 1.3310. 3. Illustrative Cases Using the FV Table: o Case 1: Solving for FV given PV, i, and n. For example, $100 invested at 12% interest over five periods grows to $176.23 (since $100 × 1.7623 = $176.23). o Case 2: Solving for n given FV, PV, and i. For instance, if $2,000 needs to grow to $3,000 at a 7% interest rate, the required time is six periods. o Case 3: Solving for i given FV, PV, and n. If $2,001 today needs to grow to $4,000 over nine years, an interest rate of approximately 8% is required. o Example Calculation To illustrate, if you win $150,000 and invest it at 8% interest to reach a goal of $555,000, the number of years (n) needed can be estimated: FV factor=555,000150,000=3.7000FV By looking up 3.7 in the 8% interest column in the FV table, we can determine the required number of years. If the table lacks this exact factor, it suggests that achieving the target amount within a reasonable time frame may not be possible with the current parameters. Summary FV calculations are essential for planning how present funds grow over time, with the compounding interest rate as a critical factor. Future value tables offer a quick reference to estimate FV across different interest rates and time periods, simplifying financial planning.