Upon taking his first job out of college,your Dad earned an annual salary of $33,000 and set a goal to earn $100,000 per year.If his salary increased at an average annual rate of 5.5%,how long did it take to reach his goal?
A)At that rate of growth,your Dad still has not earned $100,000 in a single year.
B)8.54 years
C)16.31 years
D)20.71 years

Question

Quizplus · Accepted Answer

To find out how long it takes for the salary to grow from $33,000 to $100,000 with an annual growth rate of 5.5%, we use the formula for exponential growth: $A = P(1 + r)^t$, where $A$ is the amount we're solving for ($100,000), $P$ is the initial amount ($33,000), $r$ is the rate of growth (5.5%, or 0.055 when expressed as a decimal), and $t$ is the time in years. Rearranging the formula to solve for $t$, we get $t = \frac{\log(A/P)}{\log(1 + r)}$. Plugging in the numbers, $t = \frac{\log(100,000/33,000)}{\log(1 + 0.055)}$, which calculates to approximately 20.71 years.

Upon Taking His First Job Out of College,your Dad Earned