Question

John opens a savings account with $1,000 that compounds interest daily. The APR at the time John deposits the account is 3.5%. He makes no withdrawals or deposits. What is his APY to the nearest hundredth of a percent after 1 year?

Answer 1

$\bf \qquad \qquad \textit{Annual Yield Formula} \\\\ \qquad \qquad \left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 3.5\%\to \frac{3.5}{100}\to &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, so in a year is 365} \end{array}\to &365 \end{cases} \\\\\\ \left(1+\frac{0.035}{365}\right)^{365}-1$

you'll get a decimal format, just multiply it times 100, to get the % format

Answer 2

A = P.e^(r.t)
P=1000
e = 2.71828
t=1 (one year)

A = 1000(e)³⁵/¹⁰⁰⁰

A = 1000(2.71828)³⁵/¹⁰⁰⁰ = 1035.62