Peter's Pop Quize on Effective Interest Rates

Given the following interest rates and payment periods calculate the effective interest rates. The following are given assumptions. 30 days in a month, 4 weeks in a month, 52 weeks in year, quarterly is 3 months and 365 days in a year.

1) Interest = 0.5% compounded weekly, payments are monthly
2) Interest = 12% compounded monthly, payments are every 6 months
3) Interest = 10% compounded monthly, payments are monthly
4) Interest = 5% compounded quarterly, payment is yearly

Using the equation:

(1)
\begin{align} i = (1 + {i\over P})^n-1 \end{align}

Where

  • r = the given interest rate
  • C = the number of interest payments(# of times the loan is compounded) per payment period
  • K = the number of payment periods per year.

So for # 1 the equation above becomes:

(2)
\begin{align} i = (1 + {0.005\over 4 \cdot 12})^4-1 \end{align}

i = 0.0417318%

So for # 2 the equation above becomes:

(3)
\begin{align} i = (1 + {0.12\over 6 \cdot 2})^6-1 \end{align}

i = 6.15202%

So for # 3 the equation above becomes:

(4)
\begin{align} i = (1 + {0.10\over 1\cdot 12})^1-1 \end{align}

i = 0.83333%

So for # 4 the equation above becomes:

(5)
\begin{align} i = (1 + {0.05\over 4\cdot 1})^4-1 \end{align}

i = 5.09453%

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