Question

An effective rate of 29.61% corresponds to a nominal rate,compounded weekly,of?

Answer 1

Solution

The effective annual interest rate is calculated using the following formula: $j = {\left( {1 + \frac{i}{n}} \right)^n} - 1$

Here

j - is the effective annual interest rate,

i - is the nominal interest rate,

n - is the number of periods.

Given that effective annual interest rate $j = 29.61$ %

And when compounded weekly, $n=52$ (52 weeks in a year)

 

Solving $j = {\left( {1 + \frac{i}{n}} \right)^n} - 1$ for $i$

$j = (1+\frac{i}{n})^{n}-1\\$

$j+1=(1+\frac{i}{n})^{n}\\$

$(j+1)^{\frac{1}{n}} = (1+\frac{i}{n})\\$

$\frac{i}{n}=(j+1)^{\frac{1}{n}}-1\\$

$i=n\times \left [ (j+1)^{\frac{1}{n}}-1 \right ]$

Replacing $j = 29.61$ % and $n=52$

$i=52\times \left [ (\frac{29.61}{100}+1)^{\frac{1}{52}}-1 \right ]$

i=0.2600076349\

$i=26$ %

Hence the nominal rate will be $i=26$ %