Question

a developer is preparing information for potential investors with an initial commitment of $100,000 for 2 years and has determined the relationship between the rate of return, r, and the final value, a, are related by the formula $r = \sqrt{\frac{a}{100,000}} - 1$. if the developer promises a rate of return of 7.5%, what will be the total value of the investment? round to the nearest dollar.
enter your answer in the box.
$\square$

Explanation:

Step1: Substitute the given rate of return into the formula

We know that \( r = 7.5\% = 0.075 \) and the formula is \( r=\sqrt{\frac{A}{100000}} - 1 \). Substitute \( r = 0.075 \) into the formula:
\( 0.075=\sqrt{\frac{A}{100000}} - 1 \)

Step2: Isolate the square root term

Add 1 to both sides of the equation:
\( 0.075 + 1=\sqrt{\frac{A}{100000}} \)
\( 1.075=\sqrt{\frac{A}{100000}} \)

Step3: Eliminate the square root

Square both sides of the equation:
\( (1.075)^2=\frac{A}{100000} \)
Calculate \( (1.075)^2 = 1.155625 \), so we have:
\( 1.155625=\frac{A}{100000} \)

Step4: Solve for A

Multiply both sides by 100000:
\( A = 1.155625\times100000 \)
\( A=115562.5 \)

Step5: Round to the nearest dollar

Since we need to round to the nearest dollar, and the decimal part is 0.5, we round up. So \( A = 115563 \)

Answer:

\( 115563 \)