Final answer:
To calculate the future value of a certificate of deposit (CD) with compound interest, use the formula A = P(1 + r/n)^(nt), where A is the future value, P is the initial deposit amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the given values ($10,000, 2.89%, and compounded monthly), the account balance after 5 years is approximately $11,764.40.
Step-by-step explanation:
To calculate the future value of a certificate of deposit (CD), we can use the formula:
A = P(1 + r/n)^(nt)
where:
- A = the future value of the CD
- P = the initial deposit amount
- r = the interest rate (expressed as a decimal)
- n = the number of times interest is compounded per year
- t = the number of years
Given that the initial deposit is $10,000.00, the interest rate is 2.89% (0.0289 as a decimal), and interest is compounded monthly (n=12), we can plug these values into the formula to calculate the future value of the CD after 5 years:
A = 10000(1 + 0.0289/12)^(12*5)
Now we can evaluate the expression to find the account balance:
A = 10000(1 + 0.0024067)^60
A ≈ $11,764.40