Question

Tina wants to save money for school. Tina invests $1,100 in an account that pays an interest rate of 7.25%. How many years will it take for the account to reach $6,600? Round your answer to the nearest hundredth.

Answer 1

To find out how many years it will take for the account to reach $6,600, we can use the formula for compound interest. By plugging in the given values and using logarithms to solve for 'time', we find that it will take approximately 11.18 years for the account to reach $6,600.

Step-by-step explanation:

To find out how many years it will take for the account to reach $6,600, we can use the formula for compound interest. The formula for compound interest is:

Final amount = Principal × (1 + interest rate)^time

Let's plug in the given values:

$6,600 = $1,100 × (1 + 0.0725)time

To isolate the variable 'time', we need to divide both sides of the equation by $1,100:

$6,600 ÷ $1,100 = (1 + 0.0725)^time

Now, we can use logarithms to solve for 'time'. Taking the logarithm of both sides of the equation:

log($6,600 ÷ $1,100) = log((1 + 0.0725)time)

Using the logarithm properties, we can bring down the exponent in front of the logarithm:

log($6,600 ÷ $1,100) = time × log(1 + 0.0725)

Now, we can divide both sides of the equation by log(1 + 0.0725) to solve for 'time':

log($6,600 ÷ $1,100) ÷ log(1 + 0.0725) = time

Calculating this on a calculator, we get:

time ≈ 11.18 years

Therefore, it will take approximately 11.18 years for the account to reach $6,600.

Answer 2

The amount of Tina money can be expressed in an exponent function like this:
an= $1100(1.0725)^n
The variable an represent the total money and variable n is the years needed to achieve that amount.

Then, the time needed for the money to reach $6,600 would be:

an= $1100(1.0725)^n
$6,600= $1100(1.0725)^n
$1,100(6)= $1100(1.0725)^n
6= (1.0725)^n
n= log1.075 6
n= 24.78