Meg's pension plan is an annuity with a guaranteed return of 7% interest per year (compounded monthly). She would like to retire with a pension of $90000 per month for 25 years. If she works 33 years before retiring, how much money must she and her employer deposit per month? (Round your answer to the nearest cent.)
To find out how much money Meg and her employer need to deposit per month, we can use the formula for the future value of an annuity.
The formula for the future value of an annuity is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value of the annuity,
P is the monthly deposit,
r is the interest rate per period (in this case, compounded monthly),
n is the number of periods (in this case, the number of months).
In this case, Meg would like to retire with a pension of $90000 per month for 25 years, which equals 25 * 12 = 300 months.
The interest rate is 7% per year, compounded monthly. So we need to convert it to a monthly interest rate by dividing it by 12 and converting it to a decimal:
r = 7% / 12 / 100 = 0.00583
We can substitute these values into the formula and solve for P:
90000 = P * [(1 + 0.00583)^300 - 1] / 0.00583
To solve for P, we multiply both sides by 0.00583 and then divide both sides by [(1 + 0.00583)^300 - 1]:
P = 90000 * 0.00583 / [(1 + 0.00583)^300 - 1]
Using a calculator, we can find that the value of P is approximately $274.85.
Therefore, Meg and her employer need to deposit approximately $274.85 per month into her pension plan.