Question

Karen has $20 in an account that earns 10% interest compounded annually.

To the nearest cent, how much will she have in 2 years?

Answer 1

$24.20

Explanation:

Compound interest is the amount of interest paid on the principal and accumulated interest.

Interest Formula

The compound interest formula is
`A = P(1+(r)/(n) )^(nt)`. The variables for this formula are as follows:

• A is the total amount in the account
• P is the principal or the original balance of the account.
• r is the interest rate expressed as a decimal
• n is the number of times compounded per year
• t is time in years

To find the total amount in Karen's account after 2 years, we need to define our variables and plug them into the formula.

Solving Compound Interest

Firstly, let's identify the value of each of the variables. The original amount in the account is $20. So, P = 20. Additionally, the interest rate is 10%, which is equal to 0.1. So, r = 0.1. Since interest is compounded annually, it is compounded once a year. Thus, n = 1. Finally, we want to know the amount after 2 years, so t = 2.

Now, let's plug these values into the formula above.

• 
  `A=20(1+(0.1)/(1))^(1*2)`

This can be simplified to make the equation easier to solve.

• A = 20(1.1)²

Using this equation, we can say A = 24.20. Therefore, after 2 years, Karen will have $24.20 in her account.