Question

25 years old, salary is 70,000 1. assume your nest egg is 4,504,260. since you are 25 you want to be more aggressive with investments and expect to earn 8% while saving for retirement. you were left 50,000 cash inheritance that you will invest at (8%) to help fund your nest egg. If you start saving at 25 yrs and plan to save until you retire at age 65, how much must you save each year (at the end of the year) to reach your financial goal of 4,504,260. 

Answer 1

Solution

Value of Nest egg=4504260

Now this nest egg= Future value of 50000+Future value of annuity payment made

Future value of 50000=Initial investment*(1+r)^n

where

r-intrets rate=8%

n-number of periods=40

Future value of 50000=50000*(1+.08)^40=1086226.07

Thus the Future value of annuity payment=Value of Nest egg-Future value of 50000

Future value of annuity payment=4504260-1086226.07=3418033.93

Now Future value of annuity payment=Annuity payment*(((1+r)^n)-1)/r

where

r-intrets rate=8%

n-number of periods=40

Putting values

3418033.93=Annuity payment*(((1+.08)^40)-1)/.08

Solving we get

Annuity payment=$13194.163 (Saving to be made at end of each year)