Math Problem Statement

Margo borrows $500, agreeing to pay it back with 2% annual interest after 11 months. How much interest will she pay?

Round your answer to the nearest cent, if necessary.

Solution

To calculate the interest Margo will pay, we use the formula for simple interest:

I=PrtI = P \cdot r \cdot t

Where:

  • II is the interest,
  • P=500P = 500 is the principal amount,
  • r=0.02r = 0.02 is the annual interest rate (2%),
  • t=1112t = \frac{11}{12} is the time in years (11 months).

Substitute the values:

I=5000.021112I = 500 \cdot 0.02 \cdot \frac{11}{12}

First, calculate step-by-step:

  1. 0.02500=100.02 \cdot 500 = 10,
  2. 1112=0.9167\frac{11}{12} = 0.9167,
  3. 100.9167=9.16710 \cdot 0.9167 = 9.167.

Round to the nearest cent:

I=9.17I = 9.17

Final Answer:

Margo will pay $9.17 in interest.


Do you want details or have questions?
Here are 5 related questions to expand your understanding:

  1. How does the time period affect the interest calculation in simple interest?
  2. What would the interest be if the loan duration was 1 year?
  3. How would the calculation change for compound interest instead of simple interest?
  4. What is the total amount Margo has to pay back, including the principal?
  5. How does the interest rate affect the final interest amount?

Tip: Always convert months into a fraction of a year when dealing with interest calculations.

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Math Problem Analysis

Mathematical Concepts

Simple Interest
Time Conversion (Months to Years)
Basic Arithmetic

Formulas

Simple Interest Formula: I = P * r * t

Theorems

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Suitable Grade Level

Grades 6-8