Final answer:
To calculate the value of the bank account after fifteen years with a 10% interest rate compounded annually, use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the initial deposit, r is the annual interest rate (in decimal form), n is the number of times interest is compounded per year, and t is the number of years. Substituting the given values, the bank account is worth $4045.01 after fifteen years.
Step-by-step explanation:
To calculate the value of the bank account after fifteen years, we need to determine the amount of interest earned each year. The interest is compounded annually, which means it is added to the initial deposit each year.
Let's use the formula for compound interest: A = P(1 + r/n)^(nt)
where:
- A represents the final amount in the bank account
- P represents the initial deposit
- r represents the annual interest rate (in decimal form, so 10% would be 0.10)
- n represents the number of times interest is compounded per year (since it's compounded annually, n = 1)
- t represents the number of years
Substituting the given values into the formula, we have: A = 1000(1 + 0.10/1)^(1*15) = 1000(1.10)^15 = $4045.01.
Therefore, the bank account is worth $4045.01 after fifteen years.