Math Snap

STEP 1

Assumptions1. The initial investment amount is $5,000. The interest rate is5.%
3. The interest is calculated as simple interest, not compounding4. The final investment value is $8,000

STEP 2

First, we need to find the total interest earned. We can do this by subtracting the initial investment from the final value.
$$Interest = Final\, value - Initial\, investment$$

STEP 3

Now, plug in the given values for the final value and initial investment to calculate the interest.
Interest = \($\)8,000 - \($\)5,000

STEP 4

Calculate the interest amount.
Interest = \($\)8,000 - \($\),000 = \($\)3,000

STEP 5

The formula for simple interest is$$Interest = Principal\, amount \\times Interest\, rate \\times Time$$We can rearrange this formula to solve for time$$Time = \frac{Interest}{Principal\, amount \\times Interest\, rate}$$

STEP 6

Now, plug in the given values for the interest, principal amount, and interest rate to calculate the time.
Time = \frac{\($\)3,000}{\($\)5,000 \\times5.2\%}

STEP 7

Convert the percentage to a decimal value.
$$5.2\% =0.052$$Time = \frac{\($\)3,000}{\($\)5,000 \\times0.052}

STEP 8

Calculate the time.
Time = \frac{\($\)3,000}{\($\)5,000 \\times0.052} =11.54\, years

Round the time to the nearest year.
$$Time =12\, years$$It will take12 years for the investment to reach $8,000 in value.