Suppose you put $2000 in a savings account at an APR of 8% compounded quarterly. Fill in the table below. (Calculate the interest and compound it each quarter rather than using the compound interest formula. Round your answers to the nearest cent.)

Quarter

Interest Earned

Balance

$2000.00

1 $ $
2 $ $
3 $ $
4 $ $

r = 0.08/4 = 0.02 = Quarterly % rate expressed as a decimal.

I1 = P1*r*t = 2000*0.02*1 = $40.00
I2 = P2*r*t = 2040*0.02*1 = $40.80
I3 = P3*r*t = 2080.80*0.02*1 = $41.62
I4 = P4*r*t = 2122.42*0.02*1 = $42.45

Bal. = 2000 + 164.87 = 2164.87.

Quarter | Interest Earned | Balance

--------|-----------------|---------
1 | $40.00 | $2040.00
2 | $40.80 | $2080.80
3 | $41.61 | $2122.41
4 | $42.44 | $2164.85

To calculate the interest and balance for each quarter, we need to know the formula for calculating the quarterly interest and balance. The formula for calculating the quarterly interest is:

Interest = Principal * (APR / 100) / 4

The formula for calculating the new balance is:

New Balance = Balance + Interest

Using these formulas, we can fill in the table:

Quarter Interest Earned Balance
-------------------------------------------------
1 $ 40.00 $ 2040.00
2 $ 40.50 $ 2080.50
3 $ 41.61 $ 2122.11
4 $ 42.66 $ 2164.77

Therefore, for each quarter, the interest earned and the new balance will be as follows:

Quarter 1:
Interest Earned: $40.00
Balance: $2040.00

Quarter 2:
Interest Earned: $40.50
Balance: $2080.50

Quarter 3:
Interest Earned: $41.61
Balance: $2122.11

Quarter 4:
Interest Earned: $42.66
Balance: $2164.77

To fill in the table, we need to calculate the interest earned and the balance at the end of each quarter.

First, let's calculate the interest earned for the first quarter. The formula to calculate the interest earned is:

Interest = Principal * (1 + (APR / n)) - Principal

where Principal is the initial amount, APR is the annual percentage rate, and n is the number of compounding periods per year.

In this case, Principal = $2000, APR = 8%, and since compounding is done quarterly, n = 4.

So the interest earned for the first quarter is:

Interest = $2000 * (1 + (8% / 4)) - $2000

Next, we can calculate the balance at the end of the first quarter. To do this, we add the interest earned to the Principal:

Balance = Principal + Interest

Now we can fill in the first row of the table:

Quarter: 1
Interest Earned: $_______
Balance: $_______

To fill in the remaining rows, we repeat the same calculations, adjusting the Principal and Interest values for each quarter.

For example, for the second quarter:
Principal = Balance from the previous quarter
Interest = Principal * (1 + (APR / n)) - Principal
Balance = Principal + Interest

We continue this process for each quarter, until we have filled in all the rows of the table.