Question

Algebra 2A Semester Exam
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Question
Aisha's goal is to have $7,500 invested after 4 years. How much should Aisha invest at 5.9% to reach her goal? Round to the nearest hundred. (1 point)
Aisha should invest $
.
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Answer 1

To determine how much Aisha should invest today (the present value) to have $7,500 after 4 years at an interest rate of 5.9%, we can use the formula for the future value of an investment:

\[
FV = PV(1 + r)^n
\]

Where:
- \(FV\) is the future value ($7,500)
- \(PV\) is the present value (the amount Aisha should invest)
- \(r\) is the annual interest rate (5.9% or 0.059)
- \(n\) is the number of years (4)

Rearranging the formula to solve for \(PV\):

\[
PV = \frac{FV}{(1 + r)^n}
\]

Now, plug in the values:

\[
PV = \frac{7500}{(1 + 0.059)^4}
\]

Calculating the denominator:

\[
1 + 0.059 = 1.059
\]

Now raise this to the power of 4:

\[
(1.059)^4 \approx 1.2466
\]

Now substitute back into the present value formula:

\[
PV \approx \frac{7500}{1.2466} \approx 6027.44
\]

Rounding to the nearest hundred:

Aisha should invest approximately **$6,100**.