Math Problem Statement

Compute the rate (in %) for the loan. Principal: $54,000, Time: 60 days, Interest: $873. Round the answer to the nearest tenth of a percent using ordinary interest.

Solution

To compute the interest rate (in %) for the loan, we can use the formula for simple interest:

I=P×r×tI = P \times r \times t

Where:

  • II is the interest ($873),
  • PP is the principal ($54,000),
  • rr is the rate (which we need to find),
  • tt is the time in years.

Given:

  • P=54,000P = 54,000,
  • I=873I = 873,
  • t=60360t = \frac{60}{360} (since time is 60 days, and we assume 360 days in a year for ordinary interest).

Now, solving for rr:

r=IP×tr = \frac{I}{P \times t}

Let me calculate this for you.The interest rate for the loan is 9.7%, rounded to the nearest tenth of a percent.

Would you like more details on the calculations or have any further questions?

Here are some related questions for practice:

  1. How would the interest change if the loan period were extended to 90 days?
  2. What is the formula for compound interest, and how is it different from simple interest?
  3. If the principal amount were $100,000, how would the rate change for the same interest?
  4. How can ordinary interest be calculated using a 365-day year instead of 360 days?
  5. What effect does a lower interest rate have on the total interest over a longer loan period?

Tip: When using ordinary interest, remember that the time is calculated based on a 360-day year, which simplifies some financial calculations.

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Math Problem Analysis

Mathematical Concepts

Simple Interest
Algebra

Formulas

Interest = Principal × Rate × Time
Rate = Interest / (Principal × Time)

Theorems

Ordinary interest assumption with 360 days in a year

Suitable Grade Level

Grades 9-12