## Related questions with answers

You deposit

$\$ 350$

in an account. The account earns

$\$ 17.50$

simple interest in 2.5 years. What is the annual interest rate? The annual interest rate is

Solution

VerifiedThe formula for simple interest is $I=prt$ where $I$ is the amount of interest earned for an initial deposit of $P$ dollars invested at an annual interest rate of $r$ for $t$ years.

It is given that you deposit $P=350$ dollars and earn $I=17.50$ dollars in interest after $t=2.5$ years. Therefore:

$\begin{aligned} I&=prt&&\text{Formula for simple interest.}\\ 17.50&=350r(2.5)&&\text{Substitute.}\\ 17.50&=875r&&\text{Multiply 350 and 2.5.}\\ \frac{17.50}{875}&=\frac{875r}{875}&&\text{Divide both sides by 875.}\\ 0.02&=r&&\text{Simplify.}\\ 2\%&=r&&\text{Convert to a percent.} \end{aligned}$

The annual interest rate is then $\boxed{2\%}$.

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