Question

Schmidt works out that he would need $4,000 a month during his retired years. He is currently 25 years old and plans to work until his is 65. He assumes that he would need to make withdraws for 30 years past his retirement and that he's in a 25% tax bracket. Assuming he finds an account that will offer him a 6.25% annual interest rate compounded monthly...

a) how much should he have in his account at retirement?

b) how much should he deposit monthly during his working years to ensure he meets his goal?

Answer 1

ANSWER

Monthly Annuity (P)=   $4,000  
Interest rate after tax (i)= Interest *(1-tax rate)=6.25%*(1-25%) = 4.6875%  
monthly interest rate = 4.6875%/12=   0.00390625  
No of months in 30 years = 12*30=   360  

To Calculate Retirement fund at age of 65, present value of annuity formula will be used      
Present value of annuity formula =      
(4000*(1-(1/((1+0.00390625)^360)))/0.00390625)      
=772369.6222      

Amount Required to have at Retirement is   $772,369.62  
      
Future value of monthly Savings made=   772369.6222  
Interest is same as above.

Time for savings = 40 years *12=   480  

Future value of annuity formula = P *{ (1+r)^n - 1 } / r      
772369.6222   =P*(((1+0.00390625)^480)-1)/0.00390625  
772369.6222   =P*   1407.243422
P=   548.8528922  
      
So Monthly deposit to meet his goal is   $548.85  

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