Final answer:
After making annual deposits of $1000 at the beginning of each year into an account with 2% interest compounded annually, you will have $17492.94 after 15 years.
Step-by-step explanation:
When you deposit $1000 at the beginning of each year into an account earning a 2% interest compounded annually, you are creating a series of equal payments known as an annuity. Calculating the future value of this annuity requires using the future value of an annuity formula:
FV = P × { [(1 + r)^n - 1] / r }
Where:
- FV is the future value of the annuity
- P is the payment amount per period ($1000)
- r is the interest rate per period (2% or 0.02)
- n is the number of periods (15 years)
Plugging the values into the formula yields:
FV = $1000 × { [(1 + 0.02)^15 - 1] / 0.02 }
FV = $1000 × { [(1.02)^15 - 1] / 0.02 }
FV = $1000 × { (1.349858807576003 - 1) / 0.02 }
FV = $1000 × 17.49294038
FV = $17492.94
At the end of 15 years, you will have $17492.94 in your account. Note that this formula assumes that the first deposit starts to earn interest at the end of the first period, which is one year in this scenario.