Question

The amount of money in an account after interest has been earned is $1080, the principal is $1000, and the time is 2 years. What is the annual interest rate?

Answer 1

4%

Explanation:

To calculate the annual interest rate (r), you can use the formula for compound interest:

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

Where:

A is the final amount (in this case, $1080)

P is the principal amount (in this case, $1000)

r is the annual interest rate (what we want to find)

n is the number of times interest is compounded per year (assuming it's compounded annually, so n = 1)

t is the time in years (in this case, 2 years)

Plugging in the known values:

$1080 = $1000(1 + r/1)^(1*2)

Now, let's isolate the variable r:

$1080/$1000 = (1 + r)^2

Divide both sides by $1000:

1.08 = (1 + r)^2

Now, take the square root of both sides:

√1.08 = 1 + r

1.04 = 1 + r

Subtract 1 from both sides to solve for r:

r = 1.04 - 1

r = 0.04

Now, multiply by 100 to express it as a percentage:

r = 0.04 * 100

r = 4%

So, the annual interest rate is 4%.