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Homework answers / question archive / Sepia Inc
Sepia Inc. issued bonds for $375,000 that were redeemable in 10 years. They established a sinking fund that was earning 4.25% 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. Round your answer up to the next cent b. Calculate the sinking fund balance at the end of the payment period 16. Round to the nearest cent c. Calculate the interest earned in payment period 17. Round to the nearest cent d. Calculate the amount by which the sinking fund increased in payment period 17
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
