On June 30, 2016, the Esquire Company sold some merchandise to a customer for $3
ID: 2564008 • Letter: O
Question
On June 30, 2016, the Esquire Company sold some merchandise to a customer for $35,000 and agreed to accept as payment a noninterest-bearing note with an 4% discount rate requiring the payment of $35,000 on March 31, 2017. The 4% rate is appropriate in this situation. Interest accrues on December 31st, 2016.
What is the effective interest rate on the note?
On June 30, 2016, the Esquire Company sold some merchandise to a customer for $35,000 and agreed to accept as payment a noninterest-bearing note with an 4% discount rate requiring the payment of $35,000 on March 31, 2017. The 4% rate is appropriate in this situation. Interest accrues on December 31st, 2016.
Explanation / Answer
Answer:
In case of a Zero Coupon Bond the Yield to Maturity is calulated using the below formula:
R=(Face Value/initial price)^(1/N)-1
Face Value=$35,000
Initial Value=$35,000 * 96% =$ 33,600
Since Interest Accrues on 31st December it is assumed that the interest accrues semiannually.
The interest accrues semiannually, creating exactly 1.5 accrual periods of six months each till March 31, 2017, Hence N=1.5
Now applying the formula
R=(Face Value/initial price)^(1/N)-1
=($35,000/$ 33,600)^(1/1.50)-1
= 0.027588
YTM=0.027588*2 (Multiply by 2)=0.0552
=5.52% p.a
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