Find how much should be invested to have $17,500 in 10 months at 9.5% simple interest.

To find out how much should be invested to have $17,500 in 10 months at 9.5% simple interest, we can use the simple interest formula:

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

where:
- $ A $ is the amount of money accumulated after n years, including interest.
- $ P $ is the principal amount (the initial amount of money).
- $ r $ is the annual interest rate (in decimal).
- $ t $ is the time the money is invested for (in years).

Given:
- $ A = 17,500 $
- $ r = 9.5\% = 0.095 $
- $ t = \frac{10}{12} = \frac{5}{6} $ years (since 10 months is $\frac{10}{12}$ of a year)

We need to find $ P $.

Rearranging the formula to solve for $ P $:

\[ P = \frac{A}{1 + rt} \]

Substitute the given values:

\[ P = \frac{17,500}{1 + (0.095 \times \frac{5}{6})} \]

Calculate the interest rate for the given time:

\[ 0.095 \times \frac{5}{6} = 0.0791667 \]

Then:

\[ 1 + 0.0791667 = 1.0791667 \]

Now:

\[ P = \frac{17,500}{1.0791667} \]

\[ P \approx 16,213.59 \]

Therefore, approximately \$16,213.59 should be invested to have $17,500 in 10 months at 9.5% simple interest.

Would you like details or have any questions?

Here are 5 questions you might consider asking:
1. How do you calculate compound interest for the same scenario?
2. What is the difference between simple interest and compound interest?
3. How would the calculation change if the interest rate were compounded monthly?
4. What would the interest be if the principal were \$20,000 instead?
5. Can you explain the formula used to calculate simple interest in more detail?

**Tip:** When dealing with interest rates, always convert the percentage to a decimal by dividing by 100 before using it in calculations.

Learn how to calculate simple interest to determine the amount needed to invest to reach $17,500 in 10 months at a 9.5% annual rate. This problem involves basic algebra and percentage conversion for calculating simple interest. Suitable for students in Grades 9-12.

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