How long will it take $4,000 to reach $4,500 when it grows at 8 percent per year?
A) 1.12 years
B) 1.48 years
C) 1.53 years
D) 9.00 years

Question

Quizplus · Accepted Answer

To find the time it takes for an investment to grow from $4,000 to $4,500 at an 8% annual interest rate, we use the formula for compound interest: $ A = P(1 + r)^t $. Here, $ A = 4500 $, $ P = 4000 $, and $ r = 0.08 $. Solving for $ t $, we get $ 4500 = 4000(1.08)^t $. Dividing both sides by 4000 gives $ 1.125 = 1.08^t $. Taking the natural logarithm of both sides, we have $ \ln(1.125) = t \ln(1.08) $. Solving for $ t $, we find $ t \approx 1.53 $ years.

How Long Will It Take $4,000 to Reach $4,500 When