Suppose you deposit $1500 in a savings account that pays interest at an annual rate of 6%. No money is added or withdrawn from the account. How many years will it take for the account to contain $2500?

1500(1.06)^n = 2500

1.06^n = 1.6666..
take log of both sides
log 1.06^n = log 1.6666...
n log 1.06 = log 1.6666..
n = log 1.6666.. / log 1.06 = appr 8.8 years

To find out how many years it will take for the account to contain $2500, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = the final amount ($2500)
P = the principal amount ($1500)
r = the annual interest rate (6% or 0.06)
n = the number of times interest is compounded per year (let's assume it is compounded annually)
t = the number of years we want to find

Plugging in the values, we have:
2500 = 1500(1 + 0.06/1)^(1t)

Simplifying the equation further:
2500/1500 = (1 + 0.06)^t

Dividing both sides by 1500:
5/3 = (1.06)^t

Now, we can solve for t (the number of years) by taking the logarithm of both sides of the equation. Assume we are using the base-10 logarithm (log):
log(5/3) = log(1.06)^t

Using the logarithmic property of exponents:
log(5/3) = t * log(1.06)

Now, we can calculate the value of t using a calculator:

t = log(5/3) / log(1.06)

Approximately, this gives us:

t ≈ 8.32 years

So, it will take approximately 8.32 years for the account to contain $2500.

To determine how many years it will take for the savings account to contain $2500, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = final amount in the account
P = principal amount (initial deposit)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = number of years

In this case, the final amount (A) is $2500, the principal amount (P) is $1500, and the annual interest rate (r) is 6% or 0.06 (expressed as a decimal). Since it is not mentioned how many times interest is compounded per year, we will assume it is compounded annually, so n = 1.

Let's rearrange the formula to solve for t:

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

Plugging in the values:

t = (1/1) * log(2500/1500) / log(1 + 0.06/1)

Calculating the logarithm and simplifying further:

t = log(1.67) / log(1.06)

Using a calculator:

t ≈ 11.5

Therefore, it will take approximately 11.5 years for the savings account to contain $2500.