Meg's pension plan is an annuity with a guaranteed return of 3% per year (compounded quarterly). She would like to retire with a pension of $50,000 per quarter for 10 years. If she works 22 years before retiring, how much money must she and her employer deposit each quarter? HINT [See Example 5.] (Round your answer to the nearest cent.)
24040.82
To determine how much money Meg and her employer must deposit each quarter, we can use the formula for the present value of an annuity.
The formula for the present value of an annuity is:
PV = P * (1 - (1 + r)^(-n)) / r,
where PV is the present value or the amount of money that needs to be deposited, P is the periodic payment, r is the interest rate per period, and n is the number of periods.
Given that Meg wants to retire with a pension of $50,000 per quarter for 10 years, n is 10 years * 4 quarters/year = 40 quarters. The interest rate is 3% per year compounded quarterly, so the interest rate per quarter is 3% / 4 = 0.75%.
Using the given values, we can now calculate the present value (PV) of the annuity:
PV = 50000 * (1 - (1 + 0.0075)^(-40)) / 0.0075.
Calculating this expression will give us the present value of the annuity.
To find out how much money Meg and her employer must deposit each quarter, we need to divide the present value (PV) by the number of quarters. In this case, since Meg and her employer each need to deposit an equal amount, we will divide PV by 2 to get the amount each of them must deposit.
Finally, we round the result to the nearest cent to get the final answer.
Please note that the actual calculation requires plugging in the values and using a calculator or a spreadsheet.