Question

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

Answer 1

To find out how much Uta initially invested, we can use the compound interest formula:

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

where:
- \( A \) is the total amount after time \( t \) (which is $500),
- \( P \) is the principal amount (the initial investment),
- \( r \) is the annual interest rate (6% or 0.06),
- \( t \) is the time in years (6 years).

We need to rearrange the formula to solve for \( P \):

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

Substituting the values we know into the formula:

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

Calculating \( (1 + 0.06)^6 \):

\[
(1.06)^6 \approx 1.418519
\]

Now substituting back into the formula for \( P \):

\[
P = \frac{500}{1.418519} \approx 352.48
\]

So, Uta initially invested approximately **$352.48**.

The correct answer is **$352.48**.