Calculating Future Values [LO 1]
For each of the following, compute the future value: (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
Future Value: 2,200
Interest Rate: 16%
Years: 10
Future Value: 10,353
Future Value: 23
Future Value: 17
Future Value: 108,305
Future Value: 246,382
Years: 33
The correct answer and explanation is :
To calculate the Future Value (FV), we use the standard future value formula:
$$
FV = PV \times (1 + r)^t
$$
Where:
- $FV$ = Future Value
- $PV$ = Present Value (initial amount)
- $r$ = Interest Rate (as a decimal)
- $t$ = Number of Years
Given:
- Present Value (PV) = \$2,200
- Interest Rate (r) = 16% = 0.16
- Time (t) = 10 years
Calculation:
$$
FV = 2200 \times (1 + 0.16)^{10}
$$
$$
FV = 2200 \times (1.16)^{10}
$$
$$
FV = 2200 \times 4.411
$$
$$
FV = 9,704.20
$$
✅ Correct Answer: \$9,704.20
Explanation (Approx. 300 words):
Future value (FV) is a core concept in finance and investing, reflecting how much a sum of money today will grow to at a certain interest rate over a specified period. In this case, we are given a present value of \$2,200, an annual interest rate of 16%, and a time horizon of 10 years. Using the formula $FV = PV \times (1 + r)^t$, we calculate how much the \$2,200 will grow to after 10 years of compounding annually.
Compounding means that interest is calculated on both the initial principal and on the accumulated interest from previous periods. This creates exponential growth, which is why higher interest rates and longer time periods can lead to significantly larger future values. In our example, compounding at 16% annually results in a future value of \$9,704.20, more than four times the original investment.
This calculation highlights the power of compound interest. Investors, financial planners, and savers use this formula to estimate how much an investment will be worth in the future, helping in retirement planning, education savings, and other long-term financial goals. Conversely, understanding future value also helps evaluate whether a current investment opportunity is worth it, based on future expected returns.
In real life, interest might compound more frequently (quarterly, monthly, or even daily), and adjustments may be needed for such scenarios. Nonetheless, this example serves as a solid foundation in understanding how time and interest rates affect investment growth.