math
posted by patrick .
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 5 years. If she works 21 years before retiring, how much money must she and her employer deposit each quarter?

Let's pick the date of her retirement as a reference point (focal point).
i = .03/4 = .0075
n for working period = 21(4) = 84
n for retirement period = 5(4) = 20
let her and her employer's contribution be x
So the "amount" of the contributions = Present Value of her annuities at that time.
x(1.0075^84  1)/.0075 = 50,000(1  1.0075^20)/.0075
multiply both sides by .0075
x(1.0075^84  1) = 50,000(1  1.0075^20)
x(.87320...) = 50000(.1388101...)
x = 7948.34
check my arithmetic
strange pension. So she is allowing her retirement to last only 5 years, with an annual income of appr. $200,000 ?
Looks like she is going to live it up for 5 years, and then .... ???
Respond to this Question
Similar Questions

business math
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 … 
bus math
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 … 
math
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 … 
math
Meg's pension plan is an annuity with a guaranteed return of 6% per year (compounded quarterly). She would like to retire with a pension of $50,000 per quarter for 15 years. If she works 31 years before retiring, how much money must … 
Business math
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 … 
calculus
Meg's pension plan is an annuity with a guaranteed return of 4% per year (compounded quarterly). She would like to retire with a pension of $20,000 per quarter for 10 years. If she works 30 years before retiring, how much money must … 
Math
Meg's pension plan is an annuity with a guaranteed return of 7% per year (compounded quarterly). She would like to retire with a pension of $20,000 per quarter for 15 years. If she works 31 years before retiring, how much money must … 
finance math
Meg's pension plan is an annuity with a guaranteed return of 7% interest per year (compounded annually). She would like to retire with a pension of $30000 per annum for 15 years. If she works 31 years before retiring, how much money … 
Business Math
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 26 years before retiring, how much money must … 
Business Calc
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 $30,000 per quarter for 5 years. If she works 25 years before retiring, how much money must …