Question

Suppose you are 30 years old. You plan to retire at age 67 and live forever (Ok 100 years old). You want to be able to withdraw $100,000 per year during your retirement. Assume that you will earn a starting salary of $50,000, which will grow at a 2% annual rate. Your employer contributes 5% of your annual salary to your retirement fund. Further assume that your retirement fund will be invested in a basket of well diversified indices that collectively yield an annual investment return of eight percent. Upon retirement, you plan to move your investment fund to a safer investment vehicle that yields an annual investment return of two percent. Upon your death, you want to bequeath your wealth to your favorite charity.

a) If you plan to donate $500,000 to your favorite charity, what percent of your annual salary do you need to contribute each year in order to achieve your retirement goals?

b) Use Solver to maximize the amount of donation subject to the constraint that you contribute no more than 8% of your salary each year to the retirement fund.

Answer 1

a) because you want to donate $500000 to charity, P^'=P-500000 and since you want to draw $100000 yearly,

100000=[(P-500000) x R x (1+R)^N]/[(1+R)^N-1]

where R=2%pa, N=33

=> 100000=[(P-500000) x 0.02 x (1+0.02)³³]/[(1+0.02)³³-1]

=> 92223.14= (P-500000) x 0.02 x (1+0.02)³³

=> 2398856.34 =P - 500000

=> P = 2898856.34

therefore you will require $2898856.34 by the time you retire

but if you contributions 0% of your annual income, the sum is tabulated as:

Therefore the contributions can be put into solver as:

this gives the optimized percentage as:

therefore for the required target, you must contribute a little bit above 16% of your yearly salary for the fund

b) for maximization of donation subject to the factor that you will donate a max of 8%, the solver inputs are:

this would maximize the net amount at the end as follows:

thus the maximum accumulated amount will be $1787822.49 subject to the given constraints