HELPP PLSSSSSS! I understand the steps to solve I just mess up on the numbers.

Approximately 6.3876 years

When rounding to the nearest whole number, this rounds up to 7 years.

Work Shown:

We'll use the compound interest formula

A = P*(1+r/n)^(n*t)

where,

A = amount of money after t yearsP = initial deposit amount or principalr = interest rate in decimal formn = compounding frequencyt = number of years

In this case, we know that,

A = 2P, since we want the initial amount to double. P can be any positive real number you want and it doesn't affect the answer.r = 0.11 n = 4, since we're compounding 4 times a yeart = unknown, what we want to solve for

So,

A = P*(1+r/n)^(n*t)

2P = P*(1+r/n)^(n*t)

2 = (1+r/n)^(n*t)

2 = (1+0.11/4)^(4*t)

2 = 1.0275^(4t)

Ln(2) = Ln(1.0275^(4t))

Ln(2) = 4t*Ln(1.0275)

4t*Ln(1.0275) = Ln(2)

t = Ln(2)/(4*Ln(1.0275))

t = 6.38758965414661

It takes roughly 6.3876 years for the deposit to double. If you need this to the nearest whole number, then round up to 7. We don't round to 6 because then we would come up short of the goal of doubling the deposit.