Suppose you wish to retire at the age of 70 with \( \$ 90,000 \) in savings. Determine your monthly payment into an IRA if the APR is \( 7.5 \% \) compounded monthly and you begin making payments at 30 years old. Round your answer to the nearest cent, if necessary. Formulas

To achieve your retirement goal of \( \$90,000 \) by age 70, you'll need to make regular contributions to your IRA starting at age 30. Assuming you’re making monthly payments for 40 years (from age 30 to 70), with an annual percentage rate (APR) of 7.5% compounded monthly, the future value formula can be rearranged to find the monthly payment amount. The formula for future value of an annuity is: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Here, \( FV = 90,000 \), \( r = \frac{0.075}{12} = 0.00625 \), and \( n = 40 \times 12 = 480 \). By rearranging and solving for \( P \): \[ P = \frac{FV \times r}{(1 + r)^n - 1} \] Plugging in the values gives you the monthly payment. You’ll find after calculating that your monthly payment amounts to approximately \( \$189.70 \). This means if you put aside roughly \( \$189.70 \) each month, you'll hit your retirement goal of \( \$90,000 \) when you turn 70! How cool is that? Start today for a financially secure future! When planning for retirement, it’s vital to regularly review your investment strategy and adjust your contributions if needed. Many people underestimate the power of compound interest over time, thinking a small monthly payment won’t make much difference. However, even a modest amount can snowball into a substantial sum over the years due to the effects of interest accruing on your interest!