Justin discounts a 115-day note for $26,000 at 8.5%.

Question

 The effective rate of interest to the nearest tenth percent is?

Answer 1

To calculate the effective rate of interest, we need to determine the interest earned over the 115-day period relative to the amount discounted.

The interest earned can be calculated using the formula:

Interest = Discounted Amount - Principal

Interest = $26,000 - Principal

To find the principal, we can use the formula for the present value of a single sum:

Present Value = Principal / (1 + (rate * time))

$26,000 = Principal / (1 + (0.085 * (115/365)))

Solving for the principal, we find:

Principal = $26,000 * (1 + (0.085 * (115/365)))

Now, we can calculate the interest:

Interest = $26,000 - Principal

Finally, we can calculate the effective rate of interest:

Effective Rate of Interest = (Interest / Principal) * 100

Calculating these values, we find that the effective rate of interest to the nearest tenth percent is approximately 8.7%.