Question

Question 6 of 7 Michael set up a fund that would pay his family $4,000 at the beginning of every month, in perpetuity. What was the size of the investment in the fund if it was earning 5.50% compounded semi-annually? Round to the nearest cent Next Question

Answer 1

Annual rate comoounded Semiannual=   5.50%  
effective 6 month rate of Interest = 5.5%/2=   2.75%  
no. of compounding in 6 month period(m) =   6  
      
      
Effective annual interest formula (i)= (1+r)^m-1      
2.75% = (1+i)^6 - 1      
(1+0.0275)^(1/6) = i      
i=   0.004531681718   1.0275
i= effective rate per month=   0.004531681718  
perpetuity every month=   4000  
      
Value of perpetuity due = Perpetuity + Perpetuity/Interest rate      
4000 + (4000/   0.004531681718   )
886674.5232      
      
So value of Investment fund is   $886,674.52