To calculate the future value of an investment with compound interest, we use the formula:
Future Value = Present Value * (1 + Interest Rate) ^ Number of Periods
Here, the present value is $5,000, the interest rate is 5% (which is 0.05 in decimal form), and the time period is 3 years.
Let's calculate the future value step by step:
1. Convert the interest rate from percentage to decimal:
Interest Rate = 5% = 0.05
2. Add 1 to the interest rate:
1 + Interest Rate = 1 + 0.05 = 1.05
3. Raise this value to the power of the time period (3 years):
(1 + Interest Rate) ^ Time Period = (1.05) ^ 3
4. Calculate this expression:
(1.05) ^ 3 = 1.05 * 1.05 * 1.05 ≈ 1.157625
5. Multiply the present value by this calculated value:
Future Value = Present Value * (1.05) ^ 3
Future Value = $5,000 * 1.157625 ≈ $5,788.125
Since we need to round to the nearest dollar, the future value is approximately:
Future Value ≈ $5,788
So the answer is D. $5788.
