Interest Rates

[Atomic_Sheep]

Hi Guys,
I’ve got a simple question.
Say we have two values $9,500 today and $10,000 in a years time (straight out of the book), why is the interest rate between these two values 5.26% and not 5%? I calculated 5.26% when I did the problem but I can’t explain why it’s not 5% so I don’t think I understand something.
10,000 * 100 / 9,500 = 5.26%
9,500* 100 /10,000 = 5%

 

[S2000magician]

Returns are calculated on the amount invested: the beginning value.

 

[olajideanuoluwa001]

Follow this pattern:
9500*(1+r)^n = 10,000
(1+r)^n = (10,000/9,500)
1+r = (1.05263158)^(1/n)
r = {(1.05263158)^(1/n)} - 1
so assuming annual compounding, the rate after one year will be:
r = {(1.05263158)^(1/1)} - 1
r = 1.05263158 - 1
r = 5.26%
Hope that helps.