Answer:
To find out how long it will take for an investment to double in value using simple interest, we can use the formula for simple interest:
\[ \text{Simple Interest} = \frac{P \cdot R \cdot T}{100} \]
Where:
- \( P \) is the principal amount (initial investment)
- \( R \) is the rate of interest per year
- \( T \) is the time in years
Given:
- \( P = \$3000 \)
- \( R = 5.3\% = 5.3 \)
- The investment doubles, so the final amount is \( 2P = \$6000 \)
We need to find \( T \) (time) when the investment reaches double the initial amount. Rearranging the formula to solve for time:
\[ T = \frac{100 \cdot \text{Simple Interest}}{P \cdot R} \]
The simple interest earned when the investment doubles is the final amount minus the principal amount:
\[ \text{Simple Interest} = \text{Final Amount} - \text{Principal Amount} \]
\[ \text{Simple Interest} = \$6000 - \$3000 \]
\[ \text{Simple Interest} = \$3000 \]
Now, substitute these values into the formula for time:
\[ T = \frac{100 \cdot 3000}{3000 \cdot 5.3} \]
\[ T = \frac{100 \cdot 3000}{15900} \]
\[ T = \frac{300000}{15900} \]
\[ T \approx 18.87 \text{ years} \]
Therefore, it will take approximately 18.9 years (rounded to the nearest tenth) for the investment to double in value at a 5.3% simple interest rate.
Explanation: