4 What is the annual percentage yield APY for money invested

4. What is the annual percentage yield (APY) for money invested at an annual rate of 4.45% compounded daily?

Solution

when the interest is compounded daily, N = 365, thus

APY_DAILY = (1 + r/365)³⁶⁵ - 1.

then here r=4.45%

hence (1+0.0445/365)^365 -1

(1+0.00012)^365 -1

(1.00012)^365 -1

1.0455-1

0.0455

4.5%