Math Problem Statement

Calculate the missing information for the loan. Round percents to the nearest tenth and days to the next higher day.

Solution

To solve the missing information in the loan table, we need to use the formula for simple interest:

I=P×r×t360I = P \times r \times \frac{t}{360}

Where:

  • II is the interest ($220),
  • PP is the principal ($3,300),
  • rr is the interest rate (to be calculated),
  • tt is the time (167 days).

We'll also calculate the maturity value, which is the total amount to be repaid at the end of the loan:

Maturity Value=P+I\text{Maturity Value} = P + I

Let's start by solving for the rate rr. I'll calculate that now.The interest rate rr is approximately 14.4% (rounded to the nearest tenth).

Next, we'll calculate the maturity value, which is the sum of the principal and the interest.The maturity value of the loan is $3,520.

Here are the calculated results:

  • Interest rate: 14.4%
  • Maturity value: $3,520

Would you like further details or have any questions?

Here are 5 related questions to expand the topic:

  1. How does the interest method (exact vs. ordinary) affect loan calculations?
  2. What happens to the maturity value if the interest rate is compounded instead of simple interest?
  3. How would the interest change if the loan duration was 365 days?
  4. Can you explain the difference between nominal and effective interest rates?
  5. How would increasing the principal affect the total interest paid?

Tip: When calculating simple interest, always ensure the time is properly adjusted to the appropriate year-length (360 or 365 days) depending on the loan agreement.

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Math Problem Analysis

Mathematical Concepts

Simple Interest
Percentage Calculation

Formulas

I = P * r * (t / 360)
Maturity Value = Principal + Interest

Theorems

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Suitable Grade Level

High School