Final answer:
To find the future value of Joe's IRA, we use the annuity formula for compound interest with an annual deposit of $2,000 at a 4% interest rate over 30 years. Starting early with savings is crucial as compound interest substantially increases the retirement funds over time.
Step-by-step explanation:
To calculate the future value of Joe's IRA after the 30th deposit with an annual interest rate of 4%, compounded once a year, we use the future value formula for an annuity. An annuity is a series of equal payments made at regular intervals. The formula for the future value of an annuity compounded annually is:
FV = P × {[(1 + r)^n - 1] / r}
where:
- FV is the future value of the annuity,
- P is the payment amount per period,
- r is the annual interest rate (in decimal form),
- n is the number of periods.
For Joe's IRA:
- P = $2,000 (annual deposit)
- r = 0.04 (4% annual interest rate)
- n = 30 (30 years)
Plugging these numbers into the formula, we get:
FV = $2,000 × {[(1 + 0.04)^30 - 1] / 0.04}
Calculating this gives us the future value of Joe's IRA after 30 years. It is important to note that starting early with savings and relying on the power of compound interest can significantly increase the value of retirement savings over time.