Question

7. A man makes a simple discount note for $6,200, at an ordinary bank discount rate of 8.84%, for 40 days. What is the effective interest rate? Round to the nearest tenth of a percent. (Use the bankerâs rule.)

Answer 1

The effective interest rate is approximately 8.987%.

Step-by-step explanation:

To find the effective interest rate, we need to use the banker's rule. The formula for finding the effective interest rate is:

Effective Interest Rate = (Discount Rate / (1 - Discount Rate × Time)) × 100

Plugging in the given values:

Discount Rate = 8.84% = 0.0884

Time = 40 days ÷ 365 days/year = 0.1096

Substituting these values into the formula:

Effective Interest Rate = (0.0884 / (1 - (0.0884 × 0.1096))) × 100

Calculating this gives us:

Effective Interest Rate ≈ 8.987%

Answer 2

The effective interest rate, rounded to the nearest tenth, is 0.1%.

Step-by-step explanation:

The banker's rule is the simple interest formula.

The simple interest formula is given by:

`E = P*I*t`

In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly) and t is the time, in years.

The effective interest rate is given by the following formula:

`E_(IR) = (E)/(P)`.

In this problem, we have that:

A man makes a simple discount note for $6,200, at an ordinary bank discount rate of 8.84%, for 40 days. We consider that the year has 360 days. This means that
`P = 6200, I = 0.0884, t = (40)/(360) = (1)/(9)`.

So

`E = 6200*0.0884*(1)/(9) = 60.9`

The effective interest rate is

`E_(IR) = (E)/(P) = (60.9)/(6200) = 0.0098 = 0.001`

The effective interest rate, rounded to the nearest tenth, is 0.1%.