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.)
Assuming that her rate of interest is the same on her deposits ....
i = .07/12 = .005833333...
The "amount" she has at the end of 28 years becomes the "present value" for the next 20 years
let her monthly deposit be x
x [1.00583333)^336 - 1]/.00583333 = 20000 [ 1 - 1.00853333^-240 ]/.0085333
multiply each side by that denominator and its gone
x(6.0590146) = 20000(.75239795)
x = 2483.57
are you sure it was 20,000 per mont and not 2,000?
If it was 2,000 then x = 248.36
yes 20000
thank you I get it now THANKS!
To determine the amount of money that Meg and her employer must deposit per month, we need to calculate the monthly contribution required to accumulate enough savings to provide a $20,000 monthly pension for 20 years.
The formula to calculate the monthly contribution required for an annuity is:
P = (A * r) / (1 - (1 + r)^(-n))
Where:
P = monthly contribution
A = desired monthly pension
r = interest rate per period (in this case, per month)
n = number of periods (in this case, 20 years * 12 months = 240 months)
Given:
A = $20,000
r = 7% per year = 7% / 12 months = 0.5833% per month
n = 240 months
Now let's substitute these values into the formula and calculate the monthly contribution required:
P = ($20,000 * 0.005833) / (1 - (1 + 0.005833)^(-240))
P ≈ $ 121.15
Therefore, Meg and her employer must deposit approximately $121.15 per month in order to accumulate enough savings to provide a $20,000 monthly pension for 20 years.