QuestionHow long will it take for a \$5000 investment at 5.2% simple interest to grow to \$8000? Round to the nearest year.

Studdy Solution

STEP 1

Assumptions1. The initial investment amount is $5,000. The interest rate is5.%<br />3. The interest is calculated as simple interest, not compounding4. The final investment value is$ 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.
$Time = \frac{\$3,000}{\$5,000 \\times0.052} =11.54\, years$

STEP 9

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

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