Question

Sepia Inc. issued bonds for $350,000 that were redeemable in 9 years. They established a sinking fund that was earning 4.49% compounded semi-annually to pay back the principal of the bonds on maturity. Deposits were being made to the fund at the end of every 6 months. a. Calculate the size of the periodic sinking fund deposit. $0.00 Round your answer up to the next cent b. Calculate the sinking fund balance at the end of the payment period 12. $0.00 Round to the nearest cent C. Calculate the interest earned in payment period 13. $0.00 Round to the nearest cent d. Calculate the amount by which the sinking fund increased in payment period 13. Round to the nearest cent

Answer 1

Amount of Bonds (P)=   350000  
Interest rate compounded Semiannually is 4.49% or   0.0449  
Semiannual rate (i)= 0.0449/2=   0.02245  
No. of Semiannual periods (n)= 9*2=   18  
      
Sinking fund amount calculation formula = (P * i)/((1+i)^n -1)      
(350000*0.02245)/(((1+0.02245)^18)-1)      
$15,994.13      
So size of sinking fund Deposit every six months is =   $15,994.13  
      
      
Balance at period 12 ( future value of Annuity)= Annuity*(((1+i)^n)-1)/i      
15994.13*(((1+0.02245)^12)-1)/0.02245      
$217,494.38      
Sinking fund balance at 12 period is   $217,494.38  
      
Interest earned in period 13= Balance of period 12*periodic interest rate      
217494.38*0.02245      
$4,882.75      
Interest earned in period 13 is   $4,882.75  
      
Amount by which sinking fund increased in period 13 = Sinking fund Deposit + interest earned      
15994.13+4882.75      
$20,876.88      
      
by which sinking fund increased in period 13 is   $20,876.88