To find the future value of $15,800 invested at 10% APR (Annual Percentage Rate), compounded semi-annually for 4 years, you can follow these steps:
1. First, determine the periodic interest rate. Since the APR is 10% and interest is compounded semi-annually, divide the annual rate by the number of compounding periods per year:
Annual Rate / Number of Compounding Periods = Periodic Interest Rate
10% / 2 = 5% per compounding period
2. Next, find the total number of compounding periods over 4 years. Since interest is compounded semi-annually, multiply the number of years by the number of compounding periods per year:
Number of Years * Number of Compounding Periods per Year = Total Number of Compounding Periods
4 years * 2 = 8 compounding periods
3. Use the future value formula to calculate the future value of the investment:
Future Value = Principal Amount * (1 + Periodic Interest Rate)^Total Number of Compounding Periods
Future Value = $15,800 * (1 + 5%)^8
4. Calculate the future value using the formula:
Future Value = $15,800 * (1 + 0.05)^8
Future Value = $15,800 * (1.05)^8
5. Finally, compute the future value to find the amount the investment will grow to after 4 years of compounding:
Future Value = $15,800 * 1.477455
Future Value ≈ $23,333.29
Therefore, the future value of $15,800 invested at 10% APR, compounded semi-annually for 4 years, would be approximately $23,333.29.
