An investor earned $1,462.50 on an investment of $90,000 in 65 days. Find the annual simple interest rate earned on the investment

45 Idea

To find the annual simple interest rate earned on the investment, we first need to calculate the simple interest earned in 1 year.

The formula for simple interest is:

$I = P \cdot r \cdot t$

Where:
- I is the interest earned
- P is the principal amount (initial investment)
- r is the interest rate per time period
- t is the number of time periods

In this case, we have:
$I = \$1,462.50$,
$P = \$90,000$,
$t = 65$.

To find the interest rate per time period (r), we rearrange the formula as:
$r = \frac{I}{{P \cdot t}}$

Substituting the given values into the formula, we get:
$r = \frac{\$1,462.50}{{\$90,000 \cdot 65}}$

Calculating this expression gives us:
$r \approx 0.00028$

Finally, to determine the annual simple interest rate, we multiply the interest rate per time period by the number of time periods in a year. Assuming there are 365 days in a year, we have:
$Annual \ interest \ rate = r \cdot \frac{365}{t}$

Plugging in the values, we get:
$Annual \ interest \ rate \approx 0.00028 \times \frac{365}{65}$

Calculating this expression gives us:
$Annual \ interest \ rate \approx 0.001567$

Therefore, the investor earned an annual simple interest rate of approximately 0.1567%, or 15.67%.