Question

The annual percentage yield (APY) of an investment account is a representation of the actual interest rate earned on a compounding account. It is based on a compounding period of one year. Show that the APY of an account that compounds monthly can be found with the formula APY = (a + r/12)¹² – 1.

Answer 1

Consider the annual percentage yield of an account that compound monthly is written using a formula;

APY = (1 + r/12)12 - 1

 

The formula is of the form;

APY = {A(t) – a}/a

 

Suppose a compound interest is compound monthly is;

APY = {a(1 + r/12)12(t) – a}/a

 

Simplified as follows:

APY = {a(1 + r/12)12 – a}/a

APY = (1 + r/12)12 – 1

 

Therefore, the compound interest monthly formula is same as the compound interest formula obtained compounding.

Therefore, the compound interest monthly formula is same as the compound interest formula obtained compounding.