Answer:
5.8%
Step-by-step explanation:
Current yield = 6.1%
Face value of bond = $500
Market price of bond = $475
Let the original coupon rate be CR
[tex]Current\hspace{2}yield = \frac{Coupon\hspace{2}rate* Bond\hspace{2}face\hspace{2}value}{Market\hspace{2}price}*100[/tex]
[tex]6.1 = \frac{CR*500}{475}*100[/tex]
Multiply both sides by 475
[tex]6.1 *475 = \frac{CR*500}{475}*100*475[/tex]
Cancel out the 475's from the top and bottom of the right side
[tex]6.1 *475 = CR*500*100[/tex]
[tex]2897.5 = CR*50000[/tex]
Flip the sides
[tex]CR*50000 = 2897.5[/tex]
Divide both sides by 5000
[tex]\frac{CR*50000}{50000} = \frac{2897.5}{50000}[/tex]
Cancel out 50000 from the top and bottom of the left side
[tex]CR = 0.0579[/tex]%
CR = 0.0579 * 100 [convert decimal into a percentage]
CR = 5.79 %
CR = 5.8% [rounded off to the tenth place]
