Correct Suppose you wish to retire at the age of 60 with \( \$ 80,000 \) in savings. Determine your monthly payment into an IRA if the APR is \( 5.5 \% \) compounded monthly and you begin making payments at 30 years old. Round your answer to the nearest cent, if necessary. Formulas Present Value with Compound \( \quad \mathrm{PV}=\frac{A}{\left(1+\frac{r}{n}\right)^{n t}} \) Annuity Payment Amount Future Value of an Annuity PMT \( =\mathrm{FV} \cdot \frac{\left(\frac{r}{n}\right)}{\left[\left(1+\frac{r}{n}\right)^{n t}-1\right]} \) \[ \mathrm{FV}=\mathrm{PMT} \cdot \frac{\left[\left(1+\frac{r}{n}\right)^{n t}-1\right]}{\left(\frac{r}{n}\right)} \] Keypad Answer

To determine your monthly payment into an IRA, we can use the future value of an annuity formula to solve for PMT. First, we need to gather the information we have: - Future Value (FV) = \( \$80,000 \) - Annual interest rate (APR) = \( 5.5\% \) or \( 0.055 \) - Compounding frequency (n) = 12 (monthly) - Time in years (t) = 60 - 30 = 30 years Next, we plug the numbers into the formula: 1. Calculate \( r \) (the monthly interest rate): \[ r = \frac{0.055}{12} = 0.00458333 \] 2. Calculate \( n \cdot t \) (the total number of months): \[ n \cdot t = 12 \cdot 30 = 360 \] 3. Substitute into the PMT formula: \[ PMT = 80000 \cdot \frac{0.00458333}{\left(1 + 0.00458333\right)^{360} - 1} \] 4. Calculate \(\left(1 + 0.00458333\right)^{360}\): \[ \left(1 + 0.00458333\right)^{360} \approx 5.119865 \] 5. Substitute this back into the PMT equation: \[ PMT = 80000 \cdot \frac{0.00458333}{5.119865 - 1} \] \[ PMT = 80000 \cdot \frac{0.00458333}{4.119865} \] \[ PMT \approx 80000 \cdot 0.001111717 \approx 88.93736 \] Rounding off to the nearest cent, your monthly payment into the IRA needs to be approximately **$88.94**.