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

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. Rearranging the formula to solve for $t$ , we get $t=\frac{A-P}{Pr}$ .Given: $A=\$4,000$ , $P=\$3,500$ , and $r=15\%=0.15$ per year. $t=\frac{\$4,000-\$3,500}{\$3,500\times 0.15}=\frac{\$500}{\$525}=\frac{500}{525}\approx 0.952$ .Since $t$ is in years, to convert it to months, multiply by 12: $0.952\times 12\approx 11.4$ months.