Choose the one alternative that best completes the statement or answers the question.
Solve for the indicated variable.
-$A = P ( 1 + r ) ^ { t }$ for $\mathrm { t }$
A) $t = \frac { \ln \left( \frac { A } { P } \right) } { 1 + r }$
B) $t = \frac { \ln \left( \frac { A } { P } \right) } { \ln ( 1 + r ) }$
C) $t = \frac { \ln ( A - P ) } { \ln ( 1 + r ) }$
D) $t = \frac { \ln ( P - A ) } { \ln ( 1 + r ) }$

Question

Quizplus · Accepted Answer

To solve for $t$, divide both sides by $P$ to get $\frac{A}{P} = (1 + r)^t$, then apply the natural logarithm to both sides to get $\ln\left(\frac{A}{P}\right) = \ln\left((1 + r)^t\right)$. Using the property of logarithms that allows the exponent to be brought in front, we get $\ln\left(\frac{A}{P}\right) = t \ln(1 + r)$, and solving for $t$ gives $t = \frac{\ln\left(\frac{A}{P}\right)}{\ln(1 + r)}$.

Choose the One Alternative That Best Completes the Statement or Answers