Find the payment made by the ordinary annuity with the given present value. $\$ 78,983$; monthly payments for 26 years; interest rate is $3.3 \%$, compounded monthly

Step 1 ：The problem is asking for the monthly payment of an ordinary annuity given the present value, the term of the annuity, and the interest rate. An ordinary annuity is a sequence of equal payments made at the end of each period over a fixed amount of time.

Step 2 ：The formula for the present value of an ordinary annuity is: \(PV = PMT \times \left[\frac{1 - (1 + r/n)^{-nt}}{r/n}\right]\) where: PV is the present value, PMT is the payment per period, r is the annual interest rate (in decimal form), n is the number of compounding periods per year, and t is the number of years.

Step 3 ：We can rearrange this formula to solve for PMT: \(PMT = PV / \left[\frac{1 - (1 + r/n)^{-nt}}{r/n}\right]\)

Step 4 ：We can plug in the given values into this formula to find the monthly payment. Given values are: PV = \$78983, r = 0.033, n = 12, t = 26.

Step 5 ：Substituting the given values into the formula, we get: \(PMT = 78983 / \left[\frac{1 - (1 + 0.033/12)^{-12 \times 26}}{0.033/12}\right]\)

Step 6 ：Solving the above expression, we get the monthly payment to be approximately \$377.42. This means that a monthly payment of \$377.42 would need to be made for 26 years at an interest rate of 3.3% compounded monthly in order to have a present value of \$78,983.

Step 7 ：Final Answer: The monthly payment made by the ordinary annuity is approximately \(\boxed{377.42}\)