Question

A loan of $20,000 with interest at 6.5% compounded annually is to be repaid by equal payments at the end of each year for five years. What is the periodic rate of interest?

A. 0.0065
B. None
C. 6.5
D. 1.065

Answer 1

The periodic rate of interest for a loan with a 6.5% interest rate compounded annually is 6.5%, option C. Simple interest examples illustrate how to calculate both interest payments and rates using the basic formulas for simple interest.

Step-by-step explanation:

The question pertains to the concept of compound interest in financial mathematics, where the interest rate is applied to the initial principal as well as the accumulated interest from previous periods. The periodic rate of interest refers to how often the interest is calculated and added to the account. Given that the loan interest of 6.5% is compounded annually, the periodic rate of interest is simply the nominal annual interest rate, which means the correct answer is C. 6.5.

Let's explore two examples to aid your understanding:

1. For a loan of $5,000 with a simple interest rate of 6% over three years, the total amount of interest paid would be calculated using the formula Interest = Principal × rate × time. Substituting the given numbers, it would be Interest = $5,000 × 0.06 × 3 = $900.
2. If you received $500 in simple interest on a loan of $10,000 for five years, you can find the annual interest rate by rearranging the formula: rate = Interest/(Principal × time). Plugging in the values, we get rate = $500/($10,000 × 5) = 0.01, or 1%.