Penny Paid Off A Loan With A Simple Interest Rate Of 11.2% In 6 Months. What Was The Apr?

 To find the Annual Percentage Rate (APR) when given the simple interest rate and the loan term, we can use the formula for simple interest:

Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)

Where:

  • Principal (P) is the initial amount of the loan.
  • Rate (R) is the interest rate per time period (in decimal form).
  • Time (T) is the time the money is borrowed for, expressed in years.

The APR represents the annualized interest rate charged for borrowing, so it's equivalent to the simple interest rate for a one-year period.

Given:

  • Simple interest rate (R) = 11.2% = 0.112 (in decimal form)
  • Time (T) = 6 months = 0.5 years

Let's calculate the Principal (P) using the simple interest formula:

SI = P × R × T

We rearrange the formula to solve for Principal (P):

P = SI / (R × T)

Now, we can substitute the given values into the formula:

P = SI / (R × T) P = SI / (0.112 × 0.5)

Now, we need to know the amount of interest paid (Simple Interest) to calculate the Principal.

Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)

We rearrange the formula to solve for Simple Interest (SI):

SI = P × R × T

Substitute the values:

SI = P × R × T SI = P × 0.112 × 0.5

Now, let's solve for Simple Interest (SI):

SI = P × 0.112 × 0.5 SI = 0.056P

Now, let's substitute this value of SI into the equation for Principal (P):

P = SI / (R × T) P = (0.056P) / (0.112 × 0.5)

Now, let's solve for Principal (P):

P = (0.056P) / (0.056) P = P

Since P = P, the Principal is not dependent on the interest rate or time.

Therefore, the APR will also be 11.2%.

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