Question

What is the APY on an account with an APR of 7.65% that is compounded monthly?Round to 3 decimal places.

Answer 1

The Annual Percentage Yield(APY) is expressed as

`\begin{gathered} APY=(1+(r)/(n))^n-1 \\ where \\ r=period\text{ rate} \\ n=number\text{ of compoundimg periods} \end{gathered}`

Given that

`\begin{gathered} r=7.65\%=0.0765 \\ n=12\text{ \lparen compounded monthly\rparen} \end{gathered}`

By substitution, we have

`\begin{gathered} APY=(1+(0.0765)/(12))^(12)-1 \\ =0.07924 \\ \therefore \\ APY\approx0.079\text{ \lparen3 decimal places\rparen} \end{gathered}`

Hence, we have

`0.079`