Final answer:
By using the future value formula for an ordinary annuity, it's calculated that you would have around $25,525.60 in the account on your 18th birthday, assuming a $1,000 yearly deposit with a 5% interest rate compounded annually.
Step-by-step explanation:
To calculate how much money you would have on your 18th birthday after your parents have been depositing $1,000 annually into an account earning 5% interest compounded annually, we can use the future value formula for an ordinary annuity. This type of annuity assumes that the deposit is made at the end of each period (year), which is applicable since the deposits are made on your birthday every year.
The formula for the future value of an ordinary annuity is:
FV = P × { [(1 + r)^n - 1] / r }
Where:
- FV is the future value of the annuity.
- P is the annual payment (the amount deposited each year).
- r is the annual interest rate (expressed as a decimal).
- n is the number of periods (years).
By substituting the values we have:
FV = $1,000 × { [(1 + 0.05)^18 - 1] / 0.05 }
Calculating the above expression ( (1+0.05)^18 - 1) gives us approximately 1.27628 and dividing that by 0.05 gives us 25.5256. Multiplying this result by 1,000 gives the total future value on the 18th birthday:
FV = $1,000 × 25.5256 = $25,525.60
Therefore, you will have approximately $25,525.60 in the account on your 18th birthday, due to the benefits of compound interest.