Ross Clark wishes to endow a chair in finance at his alma mater. The university indicated that it requires $200,000 per year to support the chair, and the endowment would earn 10% per year. To determine the amount Ross must give the university to fund the chair, we must determine the present value of a $200,000 perpetuity discounted at 10%. Using Equation 5.7, we can determine that the present value of a perpetuity paying $200,000 per year is $2 million when the interest rate is 10%:
PV = $200,000 ÷ 0.10 = $2,000,000
In other words, to generate $200,000 every year for an indefinite period requires $2,000,000 today if Ross Clark’s alma mater can earn 10% on its investments. If the university earns 10% interest annually on the $2,000,000, it can withdraw $200,000 per year indefinitely.
Rather than making contributions to an IRA at the end of each year, you decide to make equal contributions at the beginning of each year. Based on the information provided at MFL, solve for the future value of beginning-of-year annual IRA contributions grown until retirement.