Question

Nolan has a bond with a 6.1% yield, a bid price of $475, and a face value of $500. What is the original coupon rate of this Bond?

Answer 1

Answer: The correct answer is: 5.8%

Explanation:

Answer 2

5.8%

Explanation:

Current yield = 6.1%

Face value of bond = $500

Market price of bond = $475

Let the original coupon rate be CR

`Current\hspace{2}yield = \frac{Coupon\hspace{2}rate* Bond\hspace{2}face\hspace{2}value}{Market\hspace{2}price}*100`

`6.1 = (CR*500)/(475)*100`

Multiply both sides by 475

`6.1 *475 = (CR*500)/(475)*100*475`

Cancel out the 475's from the top and bottom of the right side

`6.1 *475 = CR*500*100`

`2897.5 = CR*50000`

Flip the sides

`CR*50000 = 2897.5`

Divide both sides by 5000

`(CR*50000)/(50000) = (2897.5)/(50000)`

Cancel out 50000 from the top and bottom of the left side

`CR = 0.0579`%

CR = 0.0579 * 100 [convert decimal into a percentage]

CR = 5.79 %

CR = 5.8% [rounded off to the tenth place]