Question

You are graduating today. Your plan is to work for Dynamo Corporation for 12 years and then start your own business. You expect to save and deposit $7,500 a year for the first 6 years and $15,000 a year for the following 6 years. You will make your first deposit one year from today. In addition, your grandfather just gave you a graduation gift of $25,000 which you will deposit immediately. If the account earns 9% compounded annually, how much will you have when you start your business 12 years from now?

This problem is worth up to 7 points. You will receive 2 "extra credit" points if you solve the entire problem correctly.

Provide all supporting calculations. Write your final answer as a complete sentence.

Answer 1

It is case of multiple Annuity, we will calculate 2 separate future vales of annuities

Annuity amount Constant per year for continuous 12 years (P) = $7500  
Total years (n)=   12  
Annual interest rate is 9% or   0.09  
      
Future value of annuity formula = P *{ (1+r)^n - 1 } / r      
7500*( ((1+0.09)^12)-1)/0.09   151055.3985  
future value of $7500 annuity for 12 years   $151,055.40  
      
Annuity amount Constant per year for next 6 years (P) = (15000-7500) = $7500  
Total years (n) =   6  
      
Annual interest rate is 9% or   0.09  
      
Future value of annuity formula = P *{ (1+r)^n - 1 } / r      
7500*( ((1+0.09)^6)-1)/0.09   56425.00924  
future value of $7509 annuity for 6 years   $56,425.01  
      
Grandfather gift today=   $25,000  
time (n)=   12  
Annual interest rate is 9% or   0.09  
      
Future value of present value = Present value*(1+i)^n      
25000*(1+0.09)^12=   $70,316.62  

Total value at 12 years=      
$151,055.40 + $56,425.01 + $70,316.62
=$277,797.03      

So at the time of start of Business we will have   $277,797.03  

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