If the interest for 4 months on a loan of $80,000 is $3,200, what is the annual interest rate?

To determine the annual interest rate, we start by understanding the relationship between the interest, principal amount, rate, and time. In this scenario, the interest accrued over 4 months on a loan of $80,000 is $3,200.

The formula for interest is:

[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} ]

Here, the principal is $80,000, and the time is 4 months. To work with an annual rate, we need to express the time in years. Since 4 months is one-third of a year, we can translate that into the fraction of time as:

[ \text{Time} = \frac{4}{12} = \frac{1}{3} \text{ years} ]

Now, we can rearrange the formula to solve for the annual interest rate (R):

[ R = \frac{\text{Interest}}{\text{Principal} \times \text{Time}} ]

Substituting in the values we have:

[ R = \frac{3200}{80000 \times \frac{1}{3}} ]

This simplifies further:

[ R = \