The time $t$ in years for an amount increasing at a rate $r$ (in decimal form) to double is given by $t(r)=\frac{\ln 2}{\ln (1+r)}$. This is called "doubling time." How long will it take for prices in the economy to double at a $4 \%$ annual inflation rate? Round to the nearest year.
A) $14 \mathrm{yr}$
B) $18 \mathrm{yr}$
C) $28 \mathrm{yr}$
D) $23 \mathrm{yr}$

Question

Quizplus · Accepted Answer

To find the doubling time at a 4% inflation rate, use $r = 0.04$ in the formula $t(r)=\frac{\ln 2}{\ln (1+r)}$. Calculating gives $t(0.04) \approx \frac{\ln 2}{\ln 1.04} \approx 17.67$, which rounds to 18 years.

The Time ttt In Years for an Amount Increasing at a Rate

The Time $t$ In Years for an Amount Increasing at a Rate