Sepia Inc. issued bonds for $425,000 that were redeemable in 6 years. They estab

Question

Sepia Inc. issued bonds for $425,000 that were redeemable in 6 years. They established a sinking fund that was earning 3.83% 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.

b. Calculate the sinking fund balance at the end of the payment period 6

c. Calculate the interest earned in payment period 7

d. Calculate the amount by which the sinking fund increased in payment period 7.

Explanation / Answer

Solution:

Given that FV = $425,000, n = 6*2 = 12 and I = 3.83%/2 = 1.915%

a. FV = PMT [(1 + i)^n-1)/i] (1 + i)

$425,000 = PMT [(1.01915^12 – 1)/0.01915] (1.01915)

$425,000 = PMT (13.34816) (1.01915)

$425,000 = PMT (13.60378)

PMT = $425,000/13.60378

PMT = $31,241.31

b. FV = PMT [(1 + i)^n-1)/i] (1 + i)

FV = $31,241.31 [(1.01915^6 – 1)/0.01915] (1.01915)

FV = $31,241.31 (6.294691) (1.01915)

FV = $31,241.31 (6.415234)

FV = $200,420.33

c. Interest earned in payment period 7 = I x (6th period fund balance + PMT)

Interest earned in payment period 7 = 0.01915 x ($200,420.33 + $31,241.31)

Interest earned in payment period 7 = $4,436.32

d. Amount by which sinking fund increased in payment period 7 = Interest earned in payment period 7 + PMT

Amount by which sinking fund increased in payment period 7 = $4,436.32 + $31,241.31

Amount by which sinking fund increased in payment period 7 = $35,677.63

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