A student invests $2,000 in a savings account with an annual interest rate of 8%, compounded semi-annually. After 5 years, the amount in the account will be __________. (Round to the nearest cent)
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to apply the compound interest formula to a real-world scenario. The key is to correctly identify the values for the principal, interest rate, number of compounding periods, and time.
Key Concept Explanation
The compound interest formula is given by:
where:
is the final amount (future value) including principal and interest,
is the initial principal,
is the annual interest rate (as a decimal),
is the number of times interest is compounded per year,
is the time the money is invested for, in years.
Step-by-step Solution
1. Identify the given values: , , (semi-annual compounding), and .
2. Substitute these values into the compound interest formula:
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