<h1>Problem</h1>
If $500 is invested at an annual interest rate of 8% per year, what will its future worth at the end of 30 years? Round answer to the nearest dollar.
<h1>Solution</h1>
We can calculate future value from present value using the equation:
<div class="math math-display"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>F</mi><mi>V</mi><mo>=</mo><mi>P</mi><mi>V</mi><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mi>i</mi><msup><mo stretchy="false">)</mo><mi>n</mi></msup></mrow><annotation encoding="application/x-tex">FV = PV(1 + i)^n</annotation></semantics></math>FV=PV(1+i)n</div>
where, <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mi>V</mi></mrow><annotation encoding="application/x-tex">FV</annotation></semantics></math>FV is future value, <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mi>V</mi></mrow><annotation encoding="application/x-tex">PV</annotation></semantics></math>PV is present value, <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math>i is the annual interest rate, and <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math>n is the number of years.
<div class="math math-display"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>F</mi><mi>V</mi><mo>=</mo><mo stretchy="false">(</mo><mi mathvariant="normal">$</mi><mn>500</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mn>0.08</mn><msup><mo stretchy="false">)</mo><mn>3</mn></msup><mn>0</mn><mo>=</mo><mo stretchy="false">(</mo><mi mathvariant="normal">$</mi><mn>500</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>10.0627</mn><mo stretchy="false">)</mo><mo>≃</mo><mi mathvariant="normal">$</mi><mn>5031</mn></mrow><annotation encoding="application/x-tex">FV = (\$500)(1 + 0.08)^30 = (\$500)(10.0627) \simeq \$5031</annotation></semantics></math>FV=($500)(1+0.08)30=($500)(10.0627)≃$5031</div>

Future Value