Final answer:
The future value of $5,000 after 1 year at a 5% interest rate is $5,250. After 20 years, using the same rate and annual compounding, the future value grows to $13,266.50.
Step-by-step explanation:
To calculate the future value of $5,000 earning 5 percent after 1 year with annual compounding, you use the formula for compound interest, which is:
Future Value = Present Value × (1 + Interest Rate)Number of Years
For 1 year, this becomes:
$5,000 × (1 + 0.05)1 = $5,000 × 1.05 = $5,250
Now, to calculate the future value of $5,000 earning 5 percent after 20 years:
$5,000 × (1 + 0.05)20
Future Value after 20 years = $5,000 × (1 + 0.05)20 = $5,000 × 2.6533 = $13,266.50
The $5,000 initially invested will grow to $13,266.50 after 20 years with an annual interest rate of 5%.