To find the discount rate that is equivalent to an 18% interest rate over a period of 2 months, we can use the relationship between the interest rate and the discount rate.
Let's define:
- \( r \) = interest rate (18% or 0.18 as a decimal)
- \( d \) = discount rate
The relationship between the two rates can be represented by the formula:
\[ d = \frac{r}{1 + r} \]
This formula gives us the discount rate when we know the interest rate.
Now, plug in \( r = 0.18 \):
\[ d = \frac{0.18}{1 + 0.18} = \frac{0.18}{1.18} \]
Calculating this:
\[ d \approx \frac{0.18}{1.18} \approx 0.1525 \]
To express this as a percentage:
\[ d \approx 0.1525 \times 100 \approx 15.25% \]
However, this 15.25% is the annual discount rate. Since the sum is due in 2 months, we can adjust this discount rate for the shorter time frame.
To find the 2-month equivalent, we can simply divide the annual discount rate by 6 (since there are 6 two-month periods in a year).
So, the 2-month discount rate is:
\[ \text{2-month discount rate} = \frac{15.25%}{6} \approx 2.54% \]
Thus, the equivalent discount rate for 2 months, given an 18% annual interest rate, is approximately 2.54%.