Although most investors probably remember performing math problems that illustrated the time value of money when they were in high school, it's easy to overlook the investing power of an IRA, particularly over the course of an investor's working career. Because the Internal Revenue Service (IRS) limits annual contributions to IRA accounts at $5,000 as of the time of publication, it's relatively easy to calculate the estimated yield on an IRA if you plan to contribute the maximum amount for your entire investing career using the future value of an annuity formula.
1. Determine the amount you intend to invest each year, and set this value to variable P. For example, an investor plans to make maximum contributions of $5,000 each year until he retires, so P = 5,000.
2. Estimate the number of years until you retire and begin drawing distributions from your IRA, and set this amount equal to n. You can't receive distributions from an IRA until you reach age 59 1/2 without incurring a penalty, and the IRS requires you to begin drawing distributions when you reach age 70 1/2. The example investor is 30 years old and plans to retire when he turns 69, so he'll make contributions for 39 years. In the example n = 39.
3. Determine the projected annual rate of return on your IRA, and set this figure, written in decimal form, as variable i. The example investor invests in an IRA that advertises a 7 percent return, so i = 0.07.
4. Plug the variables into the future value of an annuity formula: IRA value at retirement = P*[([1 + i]^n -- 1)/i] The example investor's formula looks like: IRA value = 5,000 * [([1 + 0.07]^39 -- 1)/0.07 IRA value at age 69 = $928,201.
- Investors place money into IRAs on a pre-tax basis, which allows them to leverage larger investment principals and incur higher long-term rates. Because of this, income taxes on IRA contributions are deferred until investors receive a distribution, at which time they're taxed at normal income-tax rates. For example, an investor who receives a $50,000 distribution at qualifying retirement age and has no other taxable income would be taxed at a 25 percent rate as of the time of publication, yielding a post-tax value of $37,500.
- The annuities yield formula is only accurate if investors contribute the same amount each year. If the maximum amount increases -- or contribution levels change for any other reason -- the investor must recalculate the yield using three calculations: first, the annuities yield formula for the number of years he invested with one contribution, then applying that amount to a traditional compound-interest formula for the number of years until retirement. The new annuity contribution amount must then be calculated for the remaining life of the IRA contribution cycle to determine the remaining balance. Combine these two figures to estimate retirement yields.