Find the amount of an ordinary annuity for 5 years of quarterly payments of $2,200 that earn interest at 4% per year compounded quarterly.

To find the amount of an ordinary annuity, we can use the formula:

A = P * ((1 + r)^n - 1) / r

Where:
A = Amount of the annuity
P = Payment amount
r = Interest rate per compounding period
n = Number of compounding periods

In this case, we have quarterly payments of $2,200 for 5 years with an interest rate of 4% per year compounded quarterly.

First, let's convert the annual interest rate to a quarterly interest rate. Since there are 4 quarters in a year, the quarterly interest rate would be 4% / 4 = 1% or 0.01.

Next, we need to find the number of compounding periods. Since there are 4 quarters in a year, and the annuity is for 5 years, the total number of compounding periods would be 4 * 5 = 20.

Now we can substitute the values into the formula and calculate the amount of the annuity:

A = 2200 * ((1 + 0.01)^20 - 1) / 0.01

Simplifying the equation:

A = 2200 * (1.01^20 - 1) / 0.01

Using a calculator, we can find:

A ≈ 2200 * (1.21995464467 - 1) / 0.01
≈ 2200 * 0.21995464467 / 0.01
≈ 4818.90021915

Therefore, the amount of the ordinary annuity for 5 years of quarterly payments of $2,200 that earn interest at 4% per year compounded quarterly is approximately $4,818.90.