I know that I posted a similar question yesterday, but I am still confused about how to solve this.
$1000 grows to $1440 in 2 years.
My teacher taught us a way that involved square roots. Please help if you can! Thank you soo much!
1440/1000 = 1.44 = (1+i)^2
1 + i = sqrt(1.44) = 1.2
i = 0.2 or 20% compound annual interest
The taking of a square root only works if the time on deposit is two years.
Sure, I'd be happy to help you understand how to solve this problem using square roots!
To start, let's understand the concept of compound interest. Compound interest is the interest that is calculated on both the initial principal and any previously accumulated interest. In this case, we have an initial amount of $1000 that grows to $1440 in 2 years.
Now, let's break down the steps to solve this problem using square roots:
Step 1: Determine the interest rate per period:
To calculate the interest rate per period, we need to find the ratio of the final amount to the initial amount.
Final amount / Initial amount = (1000 + x) / 1000,
where x is the interest earned.
In this case, the final amount is $1440 and the initial amount is $1000. So, the equation becomes:
1440 / 1000 = (1000 + x) / 1000.
Step 2: Simplify the equation:
1440 / 1000 = 1.44, and (1000 + x) / 1000 can be simplified to (1 + x/1000).
So, we have: 1.44 = 1 + x/1000.
Step 3: Isolate x:
Subtract 1 from both sides of the equation:
1.44 - 1 = x/1000.
0.44 = x/1000.
Step 4: Solve for x:
To solve for x, we need to isolate it. In this case, we multiply both sides by 1000:
0.44 * 1000 = x.
440 = x.
Step 5: Find the interest rate:
The interest rate per period is x divided by the initial amount. So, the interest rate is:
440 / 1000 = 0.44.
Step 6: Finding the annual interest rate:
Since we want to find the annual interest rate, and we know that there are 2 years in this case, we need to divide the interest rate by the number of periods. So, the annual interest rate is:
0.44 / 2 = 0.22.
Therefore, the annual interest rate is 22%.
By using these steps, we were able to solve the problem using square roots. I hope this explanation helps you understand the process better! If you have any additional questions, feel free to ask.