Sarah invests $2,000 in a savings account that offers 4% simple interest annually. How many years will it take for her investment to reach a total of $2,400?
Understand the Problem
The question is asking to calculate how long it will take for an investment of $2,000 to grow to $2,400 with a simple annual interest rate of 4%. We need to use the simple interest formula to solve for the time (number of years).
Answer
$5 \text{ years}$
Answer for screen readers
$T = 5 \text{ years}$
Steps to Solve
- Write down the simple interest formula
The formula for simple interest is:
$I = PRT$
Where: $I =$ Interest earned $P =$ Principal amount (initial investment) $R =$ Annual interest rate (as a decimal) $T =$ Time (in years)
- Calculate the interest earned
The interest earned is the final value of the investment minus the principal amount.
$I = $2400 - $2000 = $400$
- Plug the known values into the simple interest formula
We know $I = $400$, $P = $2000$, and $R = 4% = 0.04$. Substituting these values into the formula $I = PRT$, we get:
$$400 = $2000 \cdot 0.04 \cdot T$
- Solve for T (time)
First, simplify the right side of the equation:
$$400 = $80 \cdot T$
Now, divide both sides by $80$ to isolate $T$:
$T = \frac{$400}{$80} = 5$
$T = 5 \text{ years}$
More Information
It will take 5 years for the investment to grow to $2,400. Simple interest is rarely used in real-world financial situations, as compound interest is much more common.
Tips
A common mistake is forgetting to convert the interest rate from a percentage to a decimal before plugging it into the formula, or using the final amount ($2400) as the interest earned instead of calculating the interest earned as the difference between the final amount and the principal. Also, students may mix up the values of $P$ and $I$ in the formula.
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