Final answer:
To determine the interest earned on a $1,000 annual contribution to an IRA for 30 years at a 10% interest rate, we utilize the future value of an annuity formula. The future value comes out to $164,494. Subtracting the total contributions ($30,000), the interest earned over the 30 years is $134,494.
Step-by-step explanation:
To calculate the total amount of interest earned on an Individual Retirement Account (IRA) over 30 years with an annual contribution of $1,000 at an interest rate of 10%, compounded annually, we can use the future value of an annuity formula:
Future Value of Annuity = Pmt × × rac{× ((1 + r)^n - 1)}{r}
Where:
- Pmt is the annual payment ($1,000)
- r is the annual interest rate (0.10)
- n is the number of periods (30 years)
Plugging in the numbers, the future value of the annuity can be calculated as:
Future Value of Annuity = $1,000 × (× ((1 + 0.10)^30 - 1) / 0.10)
This results in a future value of:
Future Value of Annuity = $1,000 × 164.494
Future Value of Annuity = $164,494
The total contributions over 30 years are $1,000 × 30 = $30,000.
The interest earned is the future value of the annuity minus the total contributions:
Interest Earned = Future Value of Annuity - Total Contributions
Interest Earned = $164,494 - $30,000
Interest Earned = $134,494
Therefore, the total interest earned over the course of the 30 years, rounded to the nearest dollar, is $134,494.