Does compounding interest accrue in a linear fashion throughout a period?

[Caezar07]

For a loan that accrues daily and compounds yearly with a 10% annual interest rate, why is 100*(1+.10)^1.5 equal to 115.369, and not 115.50?


Does the future value formula not work when trying to calculate compounded interest intra-period? Does the number of periods have to be an integer?

This is a real-world problem. I'm trying to value (at an intra-period point of time) a preferred stock that pays 8% annual interest that accrues daily and compounds yearly.

 

[Deleted member 4993]

For a loan that accrues daily and compounds yearly with a 10% annual interest rate, why is 100*(1+.10)^1.5 equal to 115.369, and not 115.50?


Does the future value formula not work when trying to calculate compounded interest intra-period? Does the number of periods have to be an integer?

This is a real-world problem. I'm trying to value (at an intra-period point of time) a preferred stock that pays 8% annual interest that accrues daily and compounds yearly.

because: \(\displaystyle (1+x)^n \ne 1 + n*x\)

 

[Caezar07]

So how would I calculate interest halfway through the second year?

100*(1+.10)^2.5=126.906

But, I would think that the way the interest would actually accrue is

100*(1+.10)^2=121
Plus
121*.1*.5=6.05
Equaling
127.05

Which method is correct? What does the 126.906 figure imply? What is actually happening on a fundamental level when you try to calc future value intra-period? Why does the interest not accrue in a linear fashion?

 

[Caezar07]

This seems like a fairly simple thing to me, but nothing is making sense. Why does the interest not accrue in a linear fashion throughout each period? Can anyone help with this? If I have a security with $100 principal and 10% interest, and halfway through the second year I couldn't cash out for 115.50, I would feel cheated. Is this not the way that math works? Is there a formula that will easily calculate a total accreted value of $115.50 halfway through the second year of a security that pays 10% interest compounded annually?