Final answer:
To determine Melissa's CD value at maturity, use the compound interest formula with principal $3000, 5% annual interest, compounded quarterly over 5 years, resulting in an estimated value of $3846 on her 11th birthday.
Step-by-step explanation:
The student is asking about compound interest calculations for a Certificate of Deposit (CD).
To find out how much money Melissa's CD will be worth when it matures on her 11th birthday, we can use the compound interest formula which is A = P(1 + r/n)nt, where:
- P is the principal amount ($3000)
- r is the annual interest rate (5%, or 0.05 as a decimal)
- n is the number of times that interest is compounded per year (quarterly, so n=4)
- t is the time the money is invested for (5 years, from her 6th to her 11th birthday)
Plugging in the numbers:
A = 3000(1 + 0.05/4)(4*5)
Calculating the values inside the parentheses and then raising it to the 20th power (4 compounds per year for 5 years) gives us:
A = 3000(1 + 0.0125)20
Now we compute the amount after interest:
A ≈ 3000(1.0125)20 ≈ 3000*1.2820 ≈ $3846
The CD will be worth approximately $3846 when it matures on Melissa's 11th birthday if it compounds quarterly at a 5% interest rate.