1. A man establishes an annuity for retirement by depositing $50,000 into an account that pays 7.2% compounded monthly. Equal monthly withdrawals will be made each month for 5 years, at which time the account will have a zero balance. Each year taxes must be paid on the interest earned by the account during that year. How much interest was earned during the first year?

To calculate the interest earned during the first year of the annuity, we need to determine the amount of the equal monthly withdrawals and the remaining balance after those withdrawals.

To find the monthly withdrawals, we can use the annuity formula:

PMT = [P * r * (1 + r)^n] / [(1 + r)^n - 1]

where:
PMT = monthly payment
P = initial deposit amount = $50,000
r = annual interest rate / 12 (for monthly compounding) = 7.2% / 12 = 0.006
n = total number of periods = 5 years * 12 months/year

PMT = [50000 * 0.006 * (1 + 0.006)^(5*12)] / [(1 + 0.006)^(5*12) - 1]
PMT ≈ $914.418

So, the monthly withdrawal amount is approximately $914.42.

Now, let's find the remaining balance at the end of the first year.

First, calculate the balance after the first monthly withdrawal:

Balance after 1st withdrawal = $50,000 * (1 + 0.006) - $914.42 ≈ $50,657.29

Next, calculate the balance after the remaining 11 monthly withdrawals using the formula for compound interest:

Balance after 11 months = $50,657.29 * (1 + 0.006)^(11) ≈ $49,996.78

Finally, subtract this balance from the initial deposit amount to find the interest earned during the first year:

Interest earned during the first year = $50,000 - $49,996.78 ≈ $3.22

Therefore, the interest earned during the first year is approximately $3.22.

To find out how much interest was earned during the first year, we need to calculate the annual interest earned by the account.

First, we need to find the monthly interest rate. The annual interest rate is 7.2%, and it is compounded monthly.

Monthly interest rate = Annual interest rate / Number of compounding periods per year
Monthly interest rate = 7.2% / 12 = 0.6% = 0.006 (in decimal form)

Now, we can calculate the balance at the end of the first year.

Balance after one year = Principal Amount + Interest Earned
Balance after one year = $50,000 + ($50,000 * 0.006)

Balance after one year = $50,000 + $300 = $50,300

To find out how much interest was earned during the first year, we subtract the initial deposit from the balance.

Interest earned during the first year = Balance after one year - Principal Amount
Interest earned during the first year = $50,300 - $50,000 = $300

Therefore, $300 is the amount of interest earned during the first year.