Sepia Inc

Given,

Amount of Bonds (P)=   375000  
Interest rate compounded Semiannually = 4.25% or 0.0425  
Semiannual rate (i)= 0.0425/2=   0.02125  
No. of Semiannual periods (n)= 10*2=   20  
      

a) Computation of size of the periodic sinking fund deposit:
Size of the Periodic Sinking Fund Deposit = (P * i)/((1+i)^n -1)      
= (375000*0.02125)/(((1+0.02125)^20)-1)      
= $15,242.60
So, Size of sinking fund Deposit every six months is $15,242.60
      

b) Computation of Sinking Fund Balance at the End of the Payment Period 16:      
Balance at period 16 ( future value of Annuity)= Annuity*(((1+i)^n)-1)/i      
= 15242.60*(((1+0.02125)^16)-1)/0.02125      
= $286,884.94
Sinking fund balance at 16 period = $286,884.94
      

c) Computation of Interest earned in payment period 17:
Interest earned in period 17= Balance of period 16*Periodic interest rate      
=$286,884.94*0.02125      
=$6,096.30
Interest earned in period 17 is $6,096.30
     

d) Computation of amount by which the sinking fund increased in payment period 17:
Amount by which sinking fund increased in period 17 = Sinking fund Deposit + interest earned      
15,242.60+6,096.30
$21,338.90
      

So, sinking fund increased in period 17 is $21,338.90