Question 54687
The $5,000 is considered an annuity for which we want to find the FV; while the $42,180.53 is a lump sum for which we also want to find the future value after n number of years.

Therefore, the sum of the FV of the annuity & the future value of the lump sum should be $250,000 after n number of years.

To find the FV of an annuity:
 

FV=  c*((1+r)^n-1)/r

= 5000*(1.12^n-1)/0.12

To find the FV of a lump sum:

 

FV=  c*(1+r)^n
= 42180.53*(1.12)^n

Now:

$250,000 = 5000*(1.12^n-1)/0.12 + 42180.53*(1.12)^n

Since calculations are complicated, I have used excel to answer the problem, but you can use a financial calculator as follows:

Using your financial calculator, enter the following data:  I = 12; 
PV = -42180.53; PMT = -5000; FV = 250000; N = ?  Solve for N = 11.  It will take 
11 years for John to accumulate $250,000.