How many months would it take for $3,500 to grow to $4,000 at 15%?
A) 9.5
B) 11.4
C) 348
D) 10.0
E) 6.6

Question

Quizplus · Accepted Answer

The growth of money with interest can be calculated using the formula for compound interest, but since the problem doesn't specify the compounding period (e.g., annually, monthly), a simple interest formula can be a straightforward approach for estimation: $A = P(1 + rt)$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time the money is invested or borrowed for, in years.Given:- $P = $3,500$- $A = $4,000$- $r = 15\% = 0.15$ per yearWe need to find $t$ in years, and then convert it to months (since the answer needs to be in months).Rearranging the formula to solve for $t$, we get:$$t = \frac{A - P}{P \cdot r}$$Substituting the given values:$$t = \frac{4000 - 3500}{3500 \cdot 0.15} = \frac{500}{525} = \frac{20}{21}$$ yearsTo convert years to months, multiply by 12:$$\frac{20}{21} \times 12 = \frac{240}{21} \approx 11.4$$ monthsTherefore, it would take approximately 11.4 months for $3,500 to grow to $4,000 at an annual interest rate of 15%.

How Many Months Would It Take for $3,500 to Grow