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.
1 answer