Frank deposited $4,000 in an account that earns 5% interest compounded annually.

How much interest will the account earn after 2 years, if he makes no withdrawals or deposits?

A.$400


To determine how much interest Frank's account will earn after 2 years with an annual interest rate of 5%, compounded annually, we can use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the amount of money in the account after $ t $ years.
- $ P $ is the principal amount (the initial deposit).
- $ r $ is the annual interest rate (in decimal form).
- $ n $ is the number of times the interest is compounded per year.
- $ t $ is the time the money is invested or borrowed for, in years.

In this case:
- $ P = 4000 $
- $ r = 0.05 $ (5% interest)
- $ n = 1 $ (since the interest is compounded annually)
- $ t = 2 $ years

Let's calculate the amount $ A $ after 2 years:

\[
A = 4000 \left(1 + \frac{0.05}{1}\right)^{1 \times 2}
\]
\[
A = 4000 (1 + 0.05)^2
\]
\[
A = 4000 (1.05)^2
\]
\[
A = 4000 \times 1.1025 = 4410
\]

So, the total amount in the account after 2 years is $4,410. The interest earned is:

\[
\text{Interest} = A - P = 4410 - 4000 = 410
\]

**The interest earned after 2 years is $410.**

Do you want more details or have any questions?

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Here are 5 related questions to think about:
1. What would the interest be if the interest rate were 6% instead of 5%?
2. How much interest would be earned after 3 years instead of 2 years?
3. What if Frank made an additional deposit after 1 year? How would that affect the calculation?
4. How would the interest change if it were compounded monthly instead of annually?
5. How would the interest be affected if the initial deposit were $5,000 instead of $4,000?

**Tip:** For small time periods and moderate interest rates, compound interest grows faster than simple interest, especially as the compounding frequency increases!

Frank deposited $4,000 in an account that earns 5% interest compounded annually. How much interest will the account earn after 2 years, if he makes no withdrawals or deposits?

Learn how to calculate the compound interest on a $4,000 deposit at an annual interest rate of 5%, compounded annually over 2 years. This solution walks through the formula for compound interest and explains how the interest earned is calculated, suitable for Grades 9-12.

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