Pregunta
\begin{tabular}{l} Find the missing value. Round your answer to the nearest tenth of a percent. \\ \( \begin{array}{lll}\text { Principal } & \text { Rate } & \text { Time } \\ \$ 2000 & \square \% & 8 \text { years }\end{array} \) \\ \hline\( \$ 624 \)\end{tabular}
Ask by Coleman King. in the United States
Feb 22,2025
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The missing rate is 3.9%.
Solución
We use the simple interest formula:
Interest = Principal × Rate × Time
In this problem, the principal is $2000, the time is 8 years, and the simple interest earned is $624. Let R be the rate expressed as a decimal. Then:
624 = 2000 × R × 8
To solve for R, first multiply the principal and time:
624 = 16,000 × R
Now, divide both sides by 16,000:
R = 624 ÷ 16,000 = 0.039
Since rates are usually expressed as a percentage, convert 0.039 to a percent by multiplying by 100:
0.039 × 100 = 3.9%
Thus, the missing rate is 3.9% (rounded to the nearest tenth of a percent).
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Simplifique esta solución Beyond the Answer
To find the missing interest rate, we can use the formula for simple interest, which is: \[ I = P \times r \times t \] Where \( I \) is the interest earned, \( P \) is the principal, \( r \) is the rate (in decimal), and \( t \) is the time (in years). Here, we know: - \( I = 624 \) - \( P = 2000 \) - \( t = 8 \) We need to rearrange the formula to solve for \( r \): \[ r = \frac{I}{P \times t} \] Plugging in the known values: \[ r = \frac{624}{2000 \times 8} = \frac{624}{16000} = 0.039 \] To express the rate as a percentage, we multiply by 100: \[ r = 0.039 \times 100 = 3.9\% \] So, the missing rate rounded to the nearest tenth of a percent is **3.9%**.
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