Question

What is APY(Annual Percentage Yield)? How is the APY compounded semiannually at `15%`, different from the same amount compounded continuously at `14%`?

Answer 1

`15%` compounded semiannually is `15.5625%` annually
and
`14%` compounded continuously is `15.027%` annually

Explanation:

APY refers to how much money you earn on a deposit over a year, taking into account compounding interest.

Now `$100` compounded semiannually at `15%` is `100(1+0.15/2)^2=100xx1.075^2=115.5625` i.e. `15.5625%` annually

`$100` compounded continuously at `14%`, means

`Lt_(n->oo)100xx(1+0.14/n)^n`

= `100xxe^0.14=115.027` i.e. `15.027%` annually