Meg's pension plan is an annuity with a guaranteed return of 5% per year (compounded quarterly). She would like to retire with a pension of $10,000 per quarter for 5 years. If she works 17 years before retiring, how much money must she and her employer deposit each quarter?
HELP I DONT KNOW :(
To calculate the amount of money that Meg and her employer must deposit each quarter, we can use the formula for the present value of an annuity.
The present value of an annuity formula is:
PV = P * (1 - (1 + r)^(-n)) / r
Where:
PV = Present value (the amount of money needed to achieve a desired future value)
P = Periodic payment (the amount of money deposited each quarter)
r = Interest rate per period (in this case, 5% per year compounded quarterly, so we divide it by 4 to get the quarterly interest rate)
n = Number of periods (in this case, 5 years, so multiplied by 4 to get the number of quarters)
Let's calculate the present value of the annuity:
PV = $10,000 * (1 - (1 + (0.05/4))^(-5*4)) / (0.05/4)
Simplifying this equation gives:
PV = $10,000 * (1 - (1.0125)^(-20)) / 0.0125
Now we can solve for PV:
PV = $10,000 * (1 - 0.67255911565) / 0.0125
PV = $8,274
So the present value of the annuity is $8,274.
Now, to calculate the amount that Meg and her employer must deposit each quarter, we divide the present value by the present value factor, which is given by the formula:
PV factor = (1 - (1 + r)^(-n)) / r
PV factor = (1 - (1 + (0.05/4))^(-5*4)) / (0.05/4)
Simplifying this equation gives:
PV factor = (1 - (1.0125)^(-20)) / 0.0125
Now we can solve for PV factor:
PV factor = 0.67255911565
To calculate the deposit amount, we divide the present value by the present value factor:
Deposit amount = PV / PV factor
Deposit amount = $8,274 / 0.67255911565
Therefore, Meg and her employer must deposit approximately $12,289.73 each quarter in order to achieve her desired pension of $10,000 per quarter for 5 years.