Question

A = 500(1+0.10)^3 represents a $500 investment that Kim put in a savings account for 3 years earning an interest rate of 10%, compounded annually.

Answer 1

The expression \( A = 500(1 + 0.10)^3 \) represents the amount of money in the savings account after 3 years, taking into account the initial investment of $500, an interest rate of 10%, and annual compounding.

Here’s a step-by-step breakdown of how the formula works:

1. **Initial Investment**: \( P = 500 \)
2. **Interest Rate**: \( r = 0.10 \) (which is 10%)
3. **Number of Years**: \( t = 3 \)

Since the interest is compounded annually, the formula for compound interest can be represented as:

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

Plugging in the values:

\[
A = 500(1 + 0.10)^3
\]

Calculating further:

1. First, calculate \( 1 + 0.10 \):
\[
1 + 0.10 = 1.10
\]

2. Now, raise \( 1.10 \) to the power of 3:
\[
(1.10)^3 = 1.10 \times 1.10 \times 1.10 = 1.331
\]

3. Now, multiply this result by the initial investment of $500:
\[
A = 500 \times 1.331 = 665.50
\]

After 3 years, the total amount in Kim's savings account will be **$665.50**.