Final answer:
Melissa's $3000 CD earning 4% interest compounded semiannually will be worth approximately $4204.80 when it matures on her 13th birthday after 7 years.
Step-by-step explanation:
On Melissa's 6th birthday, she receives a $3000 Certificate of Deposit (CD) which earns 4% interest compounded semiannually. The CD will mature on her 13th birthday, so we need to calculate the amount of money that will be available at that time using the formula for compound interest.
- The principal amount (P) is $3000.
- The annual interest rate (r) is 4%, or 0.04 when expressed as a decimal.
- The number of times the interest is compounded per year (n) is 2 (since it is compounded semiannually).
- The time in years (t) is 7, since the CD will mature from when Melissa is 6 until she is 13.
The formula for the final amount (A) in a compound interest account is A = P(1 + r/n)^(nt). We substitute our values to get:
A = 3000(1 + 0.04/2)^(2*7)
A = 3000(1 + 0.02)^14
A = 3000(1.02)^14
A = 3000(1.4016)
A = $4204.80
So, on Melissa's 13th birthday, the CD would have matured to approximately $4204.80.