Basic Math Examples

$A (4000) = p {(1 + \frac{0.0025}{12})}^{n (4000)}$

Step 1

Rewrite the equation as $p {(1 + \frac{0.0025}{12})}^{n (4000)} = A (4000)$ .

$p {(1 + \frac{0.0025}{12})}^{n (4000)} = A (4000)$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Divide $0.0025$ by $12$ .

$p {(1 + 0.000208\overline{3})}^{n (4000)} = A (4000)$

Step 2.2

Add $1$ and $0.000208\overline{3}$ .

$p \cdot {1.000208\overline{3}}^{n (4000)} = A (4000)$

Step 3

Divide each term in $p \cdot {1.000208\overline{3}}^{n (4000)} = A (4000)$ by $p$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $p \cdot {1.000208\overline{3}}^{n (4000)} = A (4000)$ by $p$ .

$\frac{p \cdot {1.000208\overline{3}}^{n (4000)}}{p} = \frac{A (4000)}{p}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $p$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{p \cdot {1.000208\overline{3}}^{n (4000)}}{p} = \frac{A (4000)}{p}$

Step 3.2.1.2

Divide ${1.000208\overline{3}}^{n (4000)}$ by $1$ .

${1.000208\overline{3}}^{n (4000)} = \frac{A (4000)}{p}$

Step 3.2.2

Move $4000$ to the left of $n$ .

${1.000208\overline{3}}^{4000 n} = \frac{A (4000)}{p}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Move $4000$ to the left of $A$ .

${1.000208\overline{3}}^{4000 n} = \frac{4000 A}{p}$

Step 4

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln ({1.000208\overline{3}}^{4000 n}) = \ln (\frac{4000 A}{p})$

Step 5

Expand $\ln ({1.000208\overline{3}}^{4000 n})$ by moving $4000 n$ outside the logarithm.

$4000 n \ln (1.000208\overline{3}) = \ln (\frac{4000 A}{p})$

Step 6

Divide each term in $4000 n \ln (1.000208\overline{3}) = \ln (\frac{4000 A}{p})$ by $4000 \ln (1.000208\overline{3})$ and simplify.

Tap for more steps...

Step 6.1

Divide each term in $4000 n \ln (1.000208\overline{3}) = \ln (\frac{4000 A}{p})$ by $4000 \ln (1.000208\overline{3})$ .

$\frac{4000 n \ln (1.000208\overline{3})}{4000 \ln (1.000208\overline{3})} = \frac{\ln (\frac{4000 A}{p})}{4000 \ln (1.000208\overline{3})}$

Step 6.2

Simplify the left side.

Tap for more steps...

Step 6.2.1

Cancel the common factor of $4000$ .

Tap for more steps...

Step 6.2.1.1

Cancel the common factor.

$\frac{4000 n \ln (1.000208\overline{3})}{4000 \ln (1.000208\overline{3})} = \frac{\ln (\frac{4000 A}{p})}{4000 \ln (1.000208\overline{3})}$

Step 6.2.1.2

Rewrite the expression.

$\frac{n \ln (1.000208\overline{3})}{\ln (1.000208\overline{3})} = \frac{\ln (\frac{4000 A}{p})}{4000 \ln (1.000208\overline{3})}$

Step 6.2.2

Cancel the common factor of $\ln (1.000208\overline{3})$ .

Tap for more steps...

Step 6.2.2.1

Cancel the common factor.

$\frac{n \ln (1.000208\overline{3})}{\ln (1.000208\overline{3})} = \frac{\ln (\frac{4000 A}{p})}{4000 \ln (1.000208\overline{3})}$

Step 6.2.2.2

Divide $n$ by $1$ .

$n = \frac{\ln (\frac{4000 A}{p})}{4000 \ln (1.000208\overline{3})}$