Pregunta
Use the simple interest formula to determine the missing value. \[ p=\$ 1775, \mathrm{r}=?, \mathrm{t}=4 \text { years, } \mathrm{i}=\$ 127.80 \] \( \mathrm{r}=\square \% \) (Do not round until the final answer. Then round to one decimal place as needed.)
Ask by Nguyen Martin. in the United States
Mar 09,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The interest rate \( r \) is \( 1.8\% \).
Solución
We start with the simple interest formula:
\[
i = p \times \frac{r}{100} \times t
\]
Substitute the known values:
\[
127.80 = 1775 \times \frac{r}{100} \times 4
\]
Multiply \(1775\) by \(4\):
\[
127.80 = 7100 \times \frac{r}{100}
\]
Solve for \(\frac{r}{100}\) by dividing both sides by \(7100\):
\[
\frac{r}{100} = \frac{127.80}{7100}
\]
Now multiply both sides by \(100\) to isolate \(r\):
\[
r = 100 \times \frac{127.80}{7100}
\]
Compute the expression:
\[
r = \frac{12780}{7100} = 1.8
\]
Thus, the interest rate is:
\[
r = 1.8\%
\]
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Bonus Knowledge
To find the missing interest rate \( r \) in the simple interest formula \( I = P \times r \times t \), we can rearrange it to find \( r \): \[ r = \frac{I}{P \times t} \] Substituting the given values: \[ r = \frac{127.80}{1775 \times 4} \] Calculating the denominator: \[ 1775 \times 4 = 7100 \] Now, substituting that back: \[ r = \frac{127.80}{7100} \] Calculating \( r \): \[ r = 0.018 \text{ (approx)} \] To express \( r \) as a percentage, multiply by 100: \[ r = 0.018 \times 100 = 1.8\% \] So the interest rate \( r \) is \( 1.8\% \).

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