How much money would you have to invest to earn $650 interest in 6 months at 121/2 % p.a. simple interest?

To find the principal amount (investment) that earns $650 interest in 6 months at a simple interest rate of $12 \frac{1}{2}\%$ (12.5% p.a.), we can use the simple interest formula:

\[
I = P \times r \times t
\]

Where:
- $I$ is the interest earned (\$650),
- $P$ is the principal (amount invested, which we need to find),
- $r$ is the annual interest rate (12.5%, or 0.125 as a decimal),
- $t$ is the time in years (6 months = 0.5 years).

Now, let's rearrange the formula to solve for $P$:

\[
P = \frac{I}{r \times t}
\]

Substituting the values:

\[
P = \frac{650}{0.125 \times 0.5}
\]

Let me calculate that.The amount you would need to invest to earn $650 in interest over 6 months at a simple interest rate of 12.5% p.a. is \$10,400.

Would you like more details or have any further questions?

Here are 5 related questions to deepen understanding:
1. How is simple interest different from compound interest?
2. What would the interest be if the rate were 10% p.a. for the same time period?
3. How would the required investment change if the time period were 1 year instead of 6 months?
4. What happens to the interest earned if the interest rate doubles?
5. How can you calculate total earnings over a longer period, say 2 years, with simple interest?

**Tip:** In simple interest, interest is only calculated on the initial principal, unlike compound interest, which is calculated on both the initial principal and the accumulated interest over time.

How much money would you have to invest to earn $650 interest in 6 months at 12 1/2 % p.a. simple interest?

Learn how to calculate the principal amount required to earn $650 interest in 6 months at a 12.5% annual simple interest rate. The solution uses the simple interest formula to determine the required investment of $10,400. Suitable for students in Grades 9-10.

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