Find the periodic payment that will amount to the given sum under the given conditions. Round answe $S=\$ 90,000$, interest is $4 \%$ compounded annually, payments made at the end of each year for 5 years

Step 1 ：Rearrange the formula for the future value of an ordinary annuity to solve for PMT: \(PMT = S * r / [(1 + r)^n - 1]\)

Step 2 ：Substitute the given values into the formula: \(PMT = $90,000 * 0.04 / [(1 + 0.04)^5 - 1]\)

Step 3 ：Calculate the value: \(PMT = $90,000 * 0.04 / [1.2166529024 - 1]\)

Step 4 ：Simplify the equation: \(PMT = $90,000 * 0.04 / 0.2166529024\)

Step 5 ：\(\boxed{PMT = $16,594.89}\)

Step 6 ：Check the answer: \(S = $16,594.89 * [(1 + 0.04)^5 - 1] / 0.04\)

Step 7 ：Simplify the equation: \(S = $16,594.89 * [1.2166529024 - 1] / 0.04\)

Step 8 ：Calculate the value: \(S = $16,594.89 * 0.2166529024 / 0.04\)

Step 9 ：\(\boxed{S = $90,000}\)