Final answer:
Melissa's $4000 CD, which earns 3% interest compounded semiannually, will be worth $5072.96 when it matures on her 14th birthday.
Step-by-step explanation:
The question is asking how much money a Certificate of Deposit (CD) that was opened with $4000 on Melissa's 6th birthday will be worth when it matures on her 14th birthday. The CD earns 3% interest, compounded semiannually. To calculate the maturity value of the CD, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested or borrowed for, in years.
In this case:
- P = $4000
- r = 0.03 (3% interest as a decimal)
- n = 2 (because the interest is compounded semiannually)
- t = 14 - 6 = 8 years
Plugging the values into the formula, we get:
A = $4000(1 + 0.03/2)^(2*8)
A = $4000(1 + 0.015)^(16)
A = $4000(1.015)^16
A = $4000(1.26824)
A = $5072.96
So, the CD will be worth $5072.96 when it matures on Melissa's 14th birthday.