Question

A $1000 20-year bond with 6% annual coupons is bought to yield an annual effective rate of 6%. If the write-up in the 4th coupon is $5, find the redemption value.

Can someone please explain this step by step?

Answer 1

Solutiion:

Given

Interest = 6%

Time = 20 years

Interest = $1000 * 6%

= $1000*0.06

=$60

4th coupon write up by $5 = $60-5 = $55

year	Coupon ($) (a)	Working	Pv factor / pvaf @6% (b)	Amount    (a* b)
1-3	60	Pvaf (6% , 3) = 1/(1.06)^1 +1/(1.06)^2 + 1/(1.06)^3	2.673	160.38
4	55	pvf (6% , 4)	0.792	43.56
5-20	60	pvaf (6% , 5-20)	8.005	480.3
20	1000	pvf (6% , 20)	0.312	312
		Redumption Value		996.24

  

Pvaf (6%, 5-20) = 1/(1.06)^1 +1/(1.06)^2 + 1/(1.06)^3 + ................... + 1/(1.06)^20 - (1/(1.06)^1 +1/(1.06)^2 + 1/(1.06)^3 + 1/(1.06)^4)

= 11.470 - 2.673 - 0.792

= 8.005