Question

(Problem 17.8 from Textbook) A person at age 30 is planning for retirement at age 60. He projects that he will need $100,000 a year, disbursed a yearly basis, until age 80. Determine the uniform annual contribution (by him and his company) needed to provide these funds. Assume that the effective interest rate is 8 % yr-1 and the rate of inflation is zero. Question 1 1 pts If the person is will need $100,000 a year, disbursed a yearly basis over 20 yr, calculate the worth of the money at retirement. Question 2 1 pts Now, determine the annual contribution needed, so that the retirement fund will accrue to the amount calculated above.

Answer 1

Annuity (P)=   100000  
interest rate (i)= 8% or    0.08  
time for Annuity withdrawl (n)=    20  
      
      
Present Value of annuity formula = (Annuity *(1-(1/(1+i)^n))/i)      
100000*(1-(1/((1+0.08)^20)))/0.08      
981814.7407      
      
So worth of money needed at Retirement is   $981,814.74  
      

Answer 2
Future value required=   $981,814.74  
Time in years (n) =60-30=   30  
interest rate (i)= 8% or   0.08  
      
Future value of ordinary annuity formula = P *{ (1+i)^n - 1 } /i      
981814.74 = P*(((1+0.08)^30)-1)/0.08      
P=981814.74/   113.2832111  
8666.904223      
      
So annual Contribution needed is   $8,666.90  

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