Use A = P(1+r)^t to find the interest rate.

$2000 grows to $2420 in 2 years.

I have no idea how to go about this problem! Your help is appreciated. Thank you!!

Ah, the mysterious interest rate conundrum! Fear not, my friend, I am here to humorously guide you through this mathematical maze.

Let's break it down step by step, shall we? We have the formula A = P(1 + r)^t, where A is the final amount, P is the initial amount, r is the interest rate (in decimal form), and t is the time in years.

In this case, we know that the initial amount (P) is $2000, and after 2 years (t), it grows to $2420 (A). We need to find the interest rate (r).

So, let's plug in the values we know and solve for r:
2420 = 2000(1 + r)^2

Now, let's bring out our mathematical humor skills. We could sit here and do boring math, but where's the fun in that? Instead, let's poke a little fun at our friend, the quadratic equation.

"Why did the quadratic equation join the circus? Because it wanted to find its 'ringleader'!"

Alright, now back to business. We need to solve the quadratic equation to find the value of r.

Expanding the equation, we have:
2420 = 2000(1 + 2r + r^2)

Simplifying further:
2420 = 2000 + 4000r + 2000r^2

Brace yourself, for here comes more humor - *drumroll* - it's time to factor out the fun! We'll group the terms and rearrange the equation:

2000r^2 + 4000r + (2000 - 2420) = 0

2000r^2 + 4000r - 420 = 0

Now, we'll use our trusty quadratic formula - oh, the trustworthy formulas never let us down:

r = (-b ± √(b^2 - 4ac))/(2a)

Inserting our values, we have:

r = (-4000 ± √(4000^2 - 4*2000*(-420)))/(2*2000)

Now, the quadratic formula can be a bit tedious to calculate, so how about a quick math joke to lighten the mood?

"Why did the math book look so sad? Because it got stuck in a 'tangent'ial conversation!"

Alright, alright, let's get back on track.

Evaluating the expression under the square root sign, we get:
√(4000^2 - 4*2000*(-420)) ≈ 5194.59

Plugging everything into the formula, we get two possible solutions for r:
r = (-4000 + 5194.59)/(2*2000) ≈ 0.348
r = (-4000 - 5194.59)/(2*2000) ≈ -1.848

Now, since we're dealing with interest rates, a negative value wouldn't make much sense here. So, we take the positive value of r:

r ≈ 0.348

And there you have it, my friend! The interest rate that would make $2000 grow to $2420 in 2 years is approximately 0.348 (or 34.8% if you prefer your rates in percentage form). Ta-da!

To find the interest rate, we can rearrange the formula A = P(1+r)^t to isolate the variable r.

Given:
P = $2000
A = $2420
t = 2 years

Substituting these values into the formula, we have:
$2420 = $2000(1+r)^2

To solve for r, we need to isolate (1+r)^2 on one side of the equation. Doing this step-by-step:

1. Divide both sides of the equation by $2000:
$2420 / $2000 = (1+r)^2

2. Simplify the left side of the equation:
1.21 = (1+r)^2

3. Take the square root of both sides to eliminate the exponent:
√1.21 = √(1+r)^2

4. Simplify both sides:
1.1 = 1+r

5. Subtract 1 from both sides:
1.1 - 1 = r

6. Simplify:
r = 0.1

Therefore, the interest rate is 0.1, or 10%.

To find the interest rate in this problem, we can rearrange the formula A = P(1+r)^t and solve for r. Here's how you can do it step by step:

Step 1: Identify the given information:
- Principle amount (initial amount): P = $2000
- Final amount (after growth): A = $2420
- Time period: t = 2 years

Step 2: Replace the variables with the given values in the formula A = P(1+r)^t:
$2420 = $2000(1+r)^2

Step 3: Solve for (1+r)^2 by dividing both sides of the equation by $2000:
$2420/$2000 = (1+r)^2

Simplifying further:
1.21 = (1+r)^2

Step 4: Take the square root of both sides to solve for 1+r:
√(1.21) = √((1+r)^2)
1.1 = 1+r

Step 5: Isolate the variable 'r' by subtracting 1 from both sides of the equation:
1.1 - 1 = r
0.1 = r

So, the interest rate in this scenario is 0.1, or 10%.

To summarize, to find the interest rate, we rearranged the formula A = P(1+r)^t, substituted the given values, simplified the equation, took the square root, and then solved for 'r' by isolating the variable.

You want to solve for r

2420 = 2000 (1+r)^t
(1+r)^2 = 2420/2000 = 1.21
1+r = sqrt(1.21) = 1.10

r = 0.10 = 10%