The number of years t it takes for an investment to double if it earns r percent (as a decimal), compounded annually, $t = \frac { \ln 2 } { \ln ( 1 + r ) }$ . How long will it take for prices in the economy to double at a 13% annual inflation
Rate? Round to the nearest year.
A) 23 yr
B) 5 yr
C) 6 yr
D) 9 yr

Question

Quizplus · Accepted Answer

Using the formula $t = \frac{\ln 2}{\ln (1 + r)}$ with $r = 0.13$, we calculate $t \approx \frac{\ln 2}{\ln 1.13} \approx 5.946$, which rounds to 6 years.

The Number of Years T It Takes for an Investment t=ln⁡2ln⁡(1+r)t = \frac { \ln 2 } { \ln ( 1 + r ) }t=ln(1+r)ln2​

The Number of Years T It Takes for an Investment $t = \frac { \ln 2 } { \ln ( 1 + r ) }$