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 $20000 per month for 20 years. If she works 28 years before retiring, how much money must she and her employer deposit per month? (Round your answer to the nearest cent.)
6622.09
To calculate the amount of money Meg and her employer must deposit per month for her pension plan, we need to use the formula for the future value of an annuity.
The future value of an annuity formula is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value of the annuity
P is the monthly payment
r is the interest rate per period
n is the total number of periods
In this case, Meg wants to retire with a pension of $20,000 per month for 20 years. Since the interest is compounded monthly, the interest rate per month would be 7% divided by 12 (0.07 / 12) or 0.00583. The total number of periods (n) would be 20 years multiplied by 12 (20 * 12) or 240 months.
Now let’s substitute these values into the formula and solve for the monthly payment (P):
20,000 = P * [(1 + 0.00583)^240 - 1] / 0.00583
To solve this equation, we need to isolate P. Let's rearrange the equation:
P = 20,000 * (0.00583 / [(1 + 0.00583)^240 - 1])
Calculating this expression will give us the monthly payment Meg and her employer must deposit to meet the retirement goal. We'll round the answer to the nearest cent.