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The average percent yield (APY) of an annuity is the annual interest rate earned in agiven year that accounts for the effects of compounding. The APY acts as the interestrate for a simple interest account and is larger is than the stated interest rate on thecompound interest account. The formula to calculate the APY on an annuity after2 years isAPY = (1+ 4) -1.Where r is the stated interest rate.Step 1 of 2: Simplify the expression for APY and write it as a single rationalexpression.

The average percent yield APY of an annuity is the annual interest rate earned in agiven year that accounts for the effects of compounding The APY acts as the i class=

Respuesta :

Answer:

[tex]APY=\frac{r^{4}}{4}+r[/tex]

Explanation:

We were given that:

[tex]\begin{gathered} APY=(1+\frac{r}{2})^2-1 \\ r=interest\text{ rate} \end{gathered}[/tex]

We will simplify the formula as shown below:

[tex]\begin{gathered} APY=(1+\frac{r}{2})^2-1 \\ \text{Let's expand the bracket, we have:} \\ APY=(1+\frac{r}{2})^2-1 \\ APY=(1+\frac{r}{2})(1+\frac{r}{2})-1 \\ APY=1(1+\frac{r}{2})+\frac{r}{2}(1+\frac{r}{2})-1 \\ APY=1+\frac{r}{2}+\frac{r}{2}+\frac{r^4}{4}-1 \\ APY=1+r+\frac{r^4}{4}-1 \\ \text{Put like terms together, we have:} \\ APY=\frac{r^4}{4}+r+1-1 \\ APY=\frac{r^4}{4}+r \\ \\ \therefore APY=\frac{r^{4}}{4}+r \end{gathered}[/tex]

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