On January 1, a company issues a $100,000, three-year note that pays 9% interest annually. The...

On January 1, a company issues a $100,000, three-year note that pays 9% interest annually. The market rate on the note is 6%. How much of the note premium should the company amortize in the first year?

I know the asnwer is $2,518.85, but I am unsure how they got it.

Expert Solution

To Find the amount of premium amortised, we must first know the amount of Premium.
And to know the amount of Premium, we have to know at what price was the Notes were issued.
Step 1: Calculation of Issue Price of the note, considering 6% market interest rate:

	Note’s Face Value		Market Interest rate (applicable for period/term)
PV of	$ 100,000.00	at	6.0%	Interest rate for	3	term payments
PV of $1	0.839619283
PV of	$ 100,000.00	=	$ 100,000.00	x	0.839619283	=	$ 83,961.93	A

Interest payable per term	at	9.0%	on	$ 100,000.00
Interest payable per term	$ 9,000.00

PVAF of 1$	for	6.0%	Interest rate for	3	term payments
PVAF of 1$	2.673011949
PV of Interest payments	=	$ 9,000.00	x	2.673011949	=		$ 24,057.11	B

				Note’s Value (A+B)			$ 108,019.04

Issue Price of Note = $ 108,019.04
Step 2: Calculation of Interest Expense

Interest Expense = Issue price x Market Interest rate

= 108019.04 x 6% = $ 6,481.14

Step 3: Calculation of Cash Interest

$ 100,000 x 9% = $ 9,000

Step 4: Amortisation of Premium = Step 3 – Step 2

= $ 9000 - $ 6481.14

= $ 2,518.86 [or $ 2518.85, rounding off difference exist only]

Hence, that’s how you calculate Premium amortised (as shown in Step 4).

The difference of $ 0.01 is due to rounding off, but the I’ve explained to you the concept as to how to arrive to the answer.

ekkarill92 answered 2 years ago

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