Midterm Question EIR

Consider a 250K loan with a 6% nominal interest rate compounded weekly. The term of the loan is 10 years.
What is the effective annual interest rate of this loan?

A) 6.00%
B) 6.18%
C) .50%
D) None of the above

ANSWER
To find the effective interest rate (EIR) we use the equation:

(1)
\begin{align} EIR=\left[1+\left(\frac{i}{p}\right)\right]^{n}-1 \end{align}

Where:

  • i = nominal interest rate
  • P = number of compounding periods in nominal statement
  • N = compounding periods in desired effect period

Since we are looking for the annual interest rate, we are looking at a yearly statement, compounded weekly.

  • Since there are 52 weeks in a year, P = 52.
  • Our interest was given as 6%, or .06 so, i = 0.06.
  • There are 52 weeks in a year, so N = 52.

This gives the equation:

(2)
\begin{align} EIR=\left[1+\left(\frac{0.06}{52}\right)\right]^{52}-1 = 0.0618 \end{align}

or 6.18%

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