Final answer:
Melissa's $5000 CD, compounded quarterly at a rate of 5%, will be worth approximately $7237.45 when it matures on her 14th birthday.
Step-by-step explanation:
To determine the amount of money that will be available when Melissa's certificate of deposit (CD) matures on her 14th birthday, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A = the amount of money accumulated after n years, including interest.
- P = the principal amount (the initial amount of money).
- r = the annual interest rate (decimal).
- n = the number of times that interest is compounded per year.
- t = the time the money is invested for in years.
In Melissa's case:
- P = $5000
- r = 5% or 0.05
- n = 4 (because the interest is compounded quarterly)
- t = 14 - 6 = 8 years (from her 6th birthday to her 14th birthday)
So the formula becomes:
A = 5000(1 + 0.05/4)^(4*8)
Let's calculate it step by step:
- First, divide the annual interest rate by the number of times interest is compounded per year: 0.05 / 4 = 0.0125.
- Next, add 1 to that number: 1 + 0.0125 = 1.0125.
- Now, raise this result to the power of the total number of compounding periods: (1.0125)^(4*8) = (1.0125)^32.
- Finally, multiply this by the principal amount: 5000 * (1.0125)^32.
Using a calculator, we find:
A ≈ 5000 * 1.447489 ≈ $7237.45
Therefore, the CD will be worth approximately $7237.45 when it matures on Melissa's 14th birthday.