Finite Math Examples

$f = 110000$ ,

$r = \frac{0.06}{2}$ ,

$t = 16$

Step 1

Present value is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk.

$P V = \frac{f}{{(1 + r)}^{t}}$

Step 2

Substitute the values into the formula.

$P V = \frac{110000}{{(1 + \frac{0.06}{2})}^{16}}$

Step 3

Simplify the right side.

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Step 3.1

Simplify

$\frac{110000}{{(1 + \frac{0.06}{2})}^{16}}$ .

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Step 3.1.1

Simplify the denominator.

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Step 3.1.1.1

Write

$1$ as a fraction with a common denominator.

$P V = \frac{110000}{{(\frac{2}{2} + \frac{0.06}{2})}^{16}}$

Step 3.1.1.2

Combine the numerators over the common denominator.

$P V = \frac{110000}{{(\frac{2 + 0.06}{2})}^{16}}$

Step 3.1.1.3

Rewrite

$\frac{2 + 0.06}{2}$ in a factored form.

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Step 3.1.1.3.1

Add

$2$ and

$0.06$ .

$P V = \frac{110000}{{(\frac{2.06}{2})}^{16}}$

Step 3.1.1.3.2

Divide

$2.06$ by

$2$ .

$P V = \frac{110000}{{1.03}^{16}}$

Step 3.1.1.4

Raise

$1.03$ to the power of

$16$ .

$P V = \frac{110000}{1.60470643}$

Step 3.1.2

Divide

$110000$ by

$1.60470643$ .

$P V = 68548.36331421$