Uta invests an amount into a compound interest investment account that pays 6% a year. After six years, she withdraws her total balance of $500. Using the formula A = P (1 + r) Superscript t, how much money did Uta initially invest?
$180.00
$320.00
$352.48
$471.70

The formula for compound interest is:

\[
A = P (1 + r)^t
\]

Where:
- $ A $ is the total amount after interest (which is $500 in this case),
- $ P $ is the initial investment (what we're solving for),
- $ r $ is the annual interest rate (6% or 0.06),
- $ t $ is the number of years (6 years).

Let's rearrange the formula to solve for $ P $:

\[
P = \frac{A}{(1 + r)^t}
\]

Now, substituting the values:

\[
P = \frac{500}{(1 + 0.06)^6}
\]

Let's calculate that.Uta initially invested approximately **$352.48** in the account.

Would you like more details or have any questions?

Here are 5 related questions:
1. How does compound interest differ from simple interest?
2. What is the formula for continuous compounding?
3. How much would Uta's balance be if the interest rate was 7% instead?
4. What would happen if Uta withdrew after only 4 years?
5. Can compound interest result in exponential growth?

**Tip**: In compound interest, the frequency of compounding (yearly, monthly, etc.) can significantly affect the final amount.

Uta invests an amount into a compound interest investment account that pays 6% a year. After six years, she withdraws her total balance of $500. Using the formula A = P (1 + r)^t, how much money did Uta initially invest? $180.00, $320.00, $352.48, $471.70

Learn how to calculate the initial investment using the compound interest formula. Uta invested in an account with 6% annual interest, and after 6 years, her balance reached $500. Understand the steps to determine her original investment, approximately $352.48. This problem is suitable for high school students in Grades 9-12.

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