Question
1 Keith opened a savings account with \( \$ 400 \) and was paid simple interest at an annual rate of \( 4 \% \). When Keith closed the account, he was paid \( \$ 64 \) in in How long was the account open for, in years? If necessary, refer to the list of financial formulas.
Ask by Nunez Powers. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Keith's account was open for 4 years.
Solution
To determine how long Keith's savings account was open, we'll use the **simple interest formula**:
\[
\text{Interest} (I) = \text{Principal} (P) \times \text{Rate} (r) \times \text{Time} (t)
\]
**Given:**
- **Principal (P):** \$400
- **Annual Interest Rate (r):** 4% or 0.04 (in decimal)
- **Interest Earned (I):** \$64
**Plugging the values into the formula:**
\[
64 = 400 \times 0.04 \times t
\]
**Calculate the product of Principal and Rate:**
\[
400 \times 0.04 = 16
\]
So, the equation simplifies to:
\[
64 = 16 \times t
\]
**Solve for Time (t):**
\[
t = \frac{64}{16} = 4 \text{ years}
\]
**Answer:**
Keith's account was open for **4 years**.
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Simplify this solution The Deep Dive
To find out how long the account was open, we can use the formula for simple interest: \[ I = P \times r \times t \] Where: - \( I \) is the interest earned (\$64), - \( P \) is the principal amount (\$400), - \( r \) is the annual interest rate (4%, or 0.04 as a decimal), - \( t \) is the time in years. Now, we can rearrange the formula to solve for \( t \): \[ t = \frac{I}{P \times r} \] Plugging in the values: \[ t = \frac{64}{400 \times 0.04} = \frac{64}{16} = 4 \] So, the account was open for 4 years.
