Question
The annual percentage yield (APY) of an investment account is 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 $=\left(1+\frac{r}{12}\right)^{12}-1$
Step 1
- **Interest Rate (r)**: This is the nominal annual interest rate or stated rate on the investment, expressed as a decimal. For example, a 6% interest rate is written as 0.06. - **Compounding**: This refers to the process where the interest earned itself earns Show more…
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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 $\mathrm{APY}=\left(1+\frac{r}{12}\right)^{12}-1$
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The effective yield (or effective annual interest rate) for an Investment is the simple interest rate that would yleld at the end of one year the same amount as is ylelded by the compounded rate that is actually applied. Approximate, to the nearest $0.01 \%,$ the effective yield corresponding to an interest rate of $r \%$ per year compounded (a) quarterly and (b) continuously. $$r=12$$
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The effective yield (or effective annual interest rate) for an investment is the simple interest rate that would yield at the end of one year the same amount as is yielded by the compounded rate that is actually applied. Approximate, to the nearest $0.01 \%$, the effective yield corresponding to an interest rate of $\boldsymbol{r} \%$ per year compounded (a) quarterly and (b) continuously. $$r=12$$
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