Solve the following problem. \( \mathrm{PV}=\$ 19,799 ; \mathrm{n}=112 ; i=0.023 ; \mathrm{PMT}= \) ? \( \mathrm{PMT}=\$ \square \) (Round to two decimal places.)

To find the payment \( \mathrm{PMT} \) in a present value annuity formula, we can use the formula: \[ \mathrm{PV} = \mathrm{PMT} \times \frac{1 - (1 + i)^{-n}}{i} \] Rearranging the formula to solve for \( \mathrm{PMT} \): \[ \mathrm{PMT} = \mathrm{PV} \times \frac{i}{1 - (1 + i)^{-n}} \] Substituting the values given: - \( \mathrm{PV} = 19,799 \) - \( n = 112 \) - \( i = 0.023 \) Calculating \( 1 + i = 1.023 \), and then \( (1 + i)^{-n} = 1.023^{-112} \). Now, let's calculate it step by step: 1. Calculate \( (1.023)^{-112} \): \[ (1.023)^{-112} \approx 0.224 \] 2. Calculate \( 1 - (1 + i)^{-n} \): \[ 1 - 0.224 \approx 0.776 \] 3. Compute \( \mathrm{PMT} \): \[ \mathrm{PMT} = 19,799 \times \frac{0.023}{0.776} \approx 19,799 \times 0.0296 \approx 585.34 \] Thus, rounding to two decimal places, the final result is: \[ \mathrm{PMT} = \$ 585.34 \]