Question

a $101,000 certificate of deposit held for 90 days is worth $102,768.19. assuming simple interest, what interest rate was earned? assume 365 days in a year. the certificate of deposit earned an interest rate of % (type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Calculate the interest amount

The interest amount $I$ is the final value minus the principal. So $I = 102768.19 - 101000=1768.19$.

Step2: Use the simple - interest formula

The simple - interest formula is $I = P\times r\times t$, where $P$ is the principal amount, $r$ is the annual interest rate, and $t$ is the time in years. Here, $P = 101000$, $t=\frac{90}{365}$ years, and $I = 1768.19$. We need to solve for $r$.
First, rewrite the formula for $r$: $r=\frac{I}{P\times t}$.
Substitute the values: $r=\frac{1768.19}{101000\times\frac{90}{365}}$.

Step3: Calculate the interest rate

$r=\frac{1768.19\times365}{101000\times90}$
$r=\frac{645489.35}{9090000}\approx0.071$.
To convert to a percentage, multiply by 100: $r = 7.1\%$.

Answer:

$7.1$