A retiree invests $3,000 in a savings plan that pays 7% per year. What will the account balance be at the end of the first year?

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The retiree's account balance at the end of the first year can be calculated using the formula for simple interest:

\[
A = P(1 + rt)
\]

Where:
- $ A $ is the final amount (account balance),
- $ P $ is the initial principal (the amount invested),
- $ r $ is the interest rate (as a decimal),
- $ t $ is the time in years.

Given:
- $ P = 3000 $,
- $ r = 7\% = 0.07 $,
- $ t = 1 \text{ year} $,

Substitute these values into the formula:

\[
A = 3000(1 + 0.07 \times 1)
\]
\[
A = 3000(1 + 0.07) = 3000(1.07) = 3210
\]

So, the account balance at the end of the first year will be **$3,210**.

Would you like more details on how this formula works or have any other questions?

Here are 5 related questions you might find helpful:
1. How would the account balance change if the interest rate was 5% instead of 7%?
2. What happens to the balance if the investment is compounded monthly rather than simple interest?
3. How much interest does the retiree earn in the first year alone?
4. What would the account balance be after 2 years with the same interest rate and principal?
5. How does compounding interest differ from simple interest?

**Tip:** Always convert percentages into decimals when using them in formulas!

A retiree invests $3,000 in a savings plan that pays 7% per year. What will the account balance be at the end of the first year?

Discover how to calculate the account balance after one year for a $3,000 investment at 7% simple interest. This detailed solution uses the simple interest formula to show how much the retiree earns in interest and the total balance at the end of the year. Suitable for students in Grades 9-11.

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