finance

N

nourdz

New member
Joined
Apr 20, 2012
Messages
5
I was wondering if any of you can answer how to do the following question, thank you

2. You purchase a 10 year, 1,000 face value bond that has a 6% coupon rate (the coupons are paid semi-annually). The yield to maturity on the bond is 6% per year compounded semi-annually. Five years later you decide to sell the bond for $1,050. What is your average annual rate of return on this investment? Express your answer as a rate per year compounded semi-annually.

a) 3.00%
b) 3.42%
c) 6.47%
d) 6.86%

 
Last edited:
well since i use a graphing calculator I just input the values in rather than using a manual formula. I understood the question as finding the intrest rate that was used to get the current price of $1050. I found that the payments are $30. ((0.6*1000)/2). and since its semi annually the period is 10 instead of 5 present value is -1050 and fv 1000. I did all that and I got a different answer. Im not sure where I went wrong
 
the initial bond price would be 1000, would it not? because the coupon rate and the YTM are both %6.

It does find the internal rate of return but, I usually find the APR or Ear manually
 
When I did it on my calculator I inputed the following

n=10
i=unknown
pv=-1050
pmt=30
fv= 1000

I get %2.430748626 I than multiplied it by 2 which only gave me 4.86
I'm really confused because I have never been taught that formula
 
Oh Okay I understand where I went wrong now. Thank you so much for your help!
 
nourdz said:
I was wondering if any of you can answer how to do the following question, thank you

2. You purchase a 10 year, 1,000 face value bond that has a 6% coupon rate (the coupons are paid semi-annually). The yield to maturity on the bond is 6% per year compounded semi-annually. Five years later you decide to sell the bond for $1,050. What is your average annual rate of return on this investment? Express your answer as a rate per year compounded semi-annually.

a) 3.00%
b) 3.42%
c) 6.47%
d) 6.86%
Click to expand...

The answer is none of the ones you listed
There are 5 years left to maturity, coupon is 6%, maturity value is $1000, market price is $1050 thus the YTM is 4.86% as calculated. This tool performed the YTM Calculation

f(x) = 1000 + -1050 * (1+x)^10 + 30 [(1+x)^10 - 1]/x
f'(x) = 10 * -1050 * (1+x)^9 + 30 * (10 x (1 + x)^9 - (1 + x)^10 + 1) / (x^2)
x = 0.1
f(x) = -1245.3068
f'(x) = -22465.8351
x1 = 0.1 - -1245.3068/-22465.8351 = 0.0445688601561
Error Bound = 0.0445688601561 - 0.1 = 0.055431 > 0.000001

x1 = 0.0445688601561
f(x1) = -255.9952
f'(x1) = -13834.9105
x2 = 0.0445688601561 - -255.9952/-13834.9105 = 0.0260652917928
Error Bound = 0.0260652917928 - 0.0445688601561 = 0.018504 > 0.000001
x2 = 0.0260652917928
f(x2) = -20.3744
f'(x2) = -11685.168
x3 = 0.0260652917928 - -20.3744/-11685.168 = 0.024321679001
Error Bound = 0.024321679001 - 0.0260652917928 = 0.001744 > 0.000001
x3 = 0.024321679001
f(x3) = -0.1632
f'(x3) = -11498.4238
x4 = 0.024321679001 - -0.1632/-11498.4238 = 0.0243074871916
Error Bound = 0.0243074871916 - 0.024321679001 = 1.4E-5 > 0.000001

x4 = 0.0243074871916
f(x4) = -0
f'(x4) = -11496.9145
x5 = 0.0243074871916 - -0/-11496.9145 = 0.0243074862601
Error Bound = 0.0243074862601 - 0.0243074871916 = 0 < 0.000001
[h=5]YTM = 2.43%
Annual YTM = 4.86%[/h]
 
PennyLess has answered the wrong question. The question is the return during the first five years. PennyLess has elucidated the second five years.

n=10
i=unknown
pv=-1050
pmt=30
fv= 1000

You have pv and fv switched.

pv = -1000
fv = 1050

Then you should get it.

You should still learn what it is you are doing. The black box will not help you grow.
 
You must log in or register to reply here.
Top