744.09 = 1000/(1+r)^5 How to find r ?

[emilstyle]

I'm studying bond rates and can't understand how to find R in this: 744.09 = 1000/(1+r)^5

The example says r = 6.09%

How the **** they found it ? What's the math behind it ? I can't really figure it out

 

[topsquark]

Since you didn't say so I have to assume you don't know how to start.

Let's let y = 1 + r to make it a tad simpler. Then
[math]744.09 = \dfrac{1000}{y^5}[/math]
So
[math]y^5 = \dfrac{1000}{744.09}[/math]
Can you find y from there?

-Dan

 

[pka]

\(\displaystyle r = \sqrt[5]{{\frac{{{{10}^3}}}{{744.09}}}} - 1\)

 

[emilstyle]

Hi Dan, thank you so much for your reply.
Nope .. I did it at school over 10 years ago. I can't remember algebra at all honestly.
let me try so...

so shouldn't that be root something at 5 ?
I mean 1000/744.09 = 1.3439
Then the question is what's the number that multiplied by itself for 5 times is 1.3439 ? Which is something like 1.0xxxx (i don't have the square at 5 on my calculator)

So if y = 1.0xxxx and Y= 1+r, it means is 1,0609 which then leaves the R at 0,0609 which is 6,09% ?
is that correct ?

If it's correct, can you tell me how to calculate the root at 5 of a number in excel or on a calculator ? Cause I can't find any way to do it.. now I did it cause I already had the answer

 

[Deleted member 4993]

Hi Dan, thank you so much for your reply.
Nope .. I did it at school over 10 years ago. I can't remember algebra at all honestly.
let me try so...

so shouldn't that be root something at 5 ?
I mean 1000/744.09 = 1.3439
Then the question is what's the number that multiplied by itself for 5 times is 1.3439 ? Which is something like 1.0xxxx (i don't have the square at 5 on my calculator)

So if y = 1.0xxxx and Y= 1+r, it means is 1,0609 which then leaves the R at 0,0609 which is 6,09% ?
is that correct ?

If it's correct, can you tell me how to calculate the root at 5 of a number in excel or on a calculator ? Cause I can't find any way to do it.. now I did it cause I already had the answer

Using excel type the following in one of the cells

= (1000/744.09)^(1/5)

The above "result" will give you 1+ r

To get 'r' directly you could type in one cell:

= (1000/744.09)^(1/5) -1 ..............................................corrected

 

[emilstyle]

it worked and gave me the result. Thank you !