Answer:
The equivalent rate is of 0.093 = 9.3% a year. Gavin is wrong, because he applied the wrong formula, its not just dividing the interest rate r by the number of compoundings n, it is [tex]E = (1 + \frac{r}{n})^{n} - 1[/tex]
Step-by-step explanation:
Equivalent interest rate:
The equivalent interest rate for an amount compounded n times during a year is given by:
[tex]E = (1 + \frac{r}{n})^{n} - 1[/tex]
In which r is the interest rate and n is the number of compoundings during an year.
Compounded annually at an interest rate of 9%
This means that [tex]r = 0.09[/tex]
Compounded quarterly:
This means that [tex]n = 4[/tex]
Equivalent rate:
[tex]E = (1 + \frac{0.09}{4})^{4} - 1 = 0.093[/tex]
The equivalent rate is of 0.093 = 9.3% a year. Gavin is wrong, because he applied the wrong formula, its not just dividing the interest rate r by the number of compoundings n, it is [tex]E = (1 + \frac{r}{n})^{n} - 1[/tex]
