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Renee wants to invest $3000 in a savings account that pays 5.3% simple interest. How long will it take for this investment to double in value? Round your answer to the nearest tenth.

User JacobJacox
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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:

User MrKodx
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