Question

2.

a)

Abigail set up a fund that would pay her family $3,000 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

b)

Answer 1

A.

Rate for Semiannual = 5.5%/2=   0.0275  
Number of months in 6 months=   6  
Effective semiannual interest rate = ((1+ monthly rate)^m)-1      
0.0275 = ((1+r)^6)-1      
1.0275= (1+r)^6      
(1+r)= (1.0275)^(1/6)      
r=   1.004531682   -1
r=   0.004531681718  
Monthly Perpetuity=   3000  
Value of Perpetuity due = Annuity +(Annuity/r)      
3000+(3000/0.004531681718)      
665005.8924      
So size of Investment in Fund is   $665,005.89  
      
B.

Semiannual rate=4%/2=   0.02  
No of compounding in year (m)=   2  
      
Effective Annual interest rate = ((1+ Semiannual rate)^m)-1      
((1+0.02)^2)-1      
0.0404      
Price of dividend = Dividend/annual required Return      
281= D/0.0404      
D = 281*0.0404=   11.3524  
So Dividend is    $11.35