QuestionOn Melissa's 6th birthday, she gets a that earns interest, compounded semiannually. If the CD matures on her 14th birthday, how much money will be available?
The amount available will be
\\square$
(Simplify your answer. Round to the nearest cent.)
Studdy Solution
STEP 1
1. Melissa receives a \$5000 CD on her 6th birthday.
2. The interest rate is 4% per annum.
3. The interest is compounded semiannually.
4. The CD matures on her 14th birthday.
5. We need to calculate the total amount available when the CD matures.
STEP 2
1. Determine the number of compounding periods.
2. Calculate the interest rate per compounding period.
3. Use the compound interest formula to find the maturity amount.
4. Simplify and round the final answer to the nearest cent.
STEP 3
Determine the number of compounding periods.
Since the CD matures on her 14th birthday and was started on her 6th birthday, the total number of years is:
Since the interest is compounded semiannually, there are 2 compounding periods per year. Therefore, the total number of compounding periods is:
STEP 4
Calculate the interest rate per compounding period.
The annual interest rate is 4%, so the interest rate per compounding period is:
Convert this percentage to a decimal for calculation:
STEP 5
Use the compound interest formula to find the maturity amount.
The compound interest formula is:
Where:
- is the amount of money accumulated after n years, including interest.
- is the principal amount (\$5000).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time in years.
Substitute the known values into the formula:
STEP 6
Simplify and round the final answer to the nearest cent.
Calculate the expression:
Using a calculator:
The amount available when the CD matures is:
\$ \boxed{6864.00}
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