Question

Gavin deposited money into his savings account that is compounded annually at an interest rate of 9%. Gavin thought the equivalent quarterly interest rate would be 2.25%. Is Gavin correct? If he is, explain why. If he is not correct, state what the equivalent quarterly interest rate is and show how you got your answer.

Answer 1

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 $E = (1 + \frac{r}{n})^{n} - 1$

Step-by-step explanation:

Equivalent interest rate:

The equivalent interest rate for an amount compounded n times during a year is given by:

$E = (1 + \frac{r}{n})^{n} - 1$

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 $r = 0.09$

Compounded quarterly:

This means that $n = 4$

Equivalent rate:

$E = (1 + \frac{0.09}{4})^{4} - 1 = 0.093$

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 $E = (1 + \frac{r}{n})^{n} - 1$