Question

Carolyn maintains an average monthly balance of $670 in her checking account. If her bank charges $7 per month as a minimum service fee, what would the annual interest rate need to be to just cover the monthly service fee?

Answer 1

Answer:

$r=12.54\%$

Explanation:

Simple Interest

There are two common approaches in finance: Simple interest and compound interest. In the simple interest investment, the interests earned in a certain period are not added as part of the next investment period, i.e. it's equivalent to the account holder to withdraw the interest for each period.

The compound interest computes the interests earned in a period, adds it to the investment and computes the next interests including the previous interests.

The situation in the question requires us to compute the annual interest rate so the average monthly balance on Carolyn's account pays the fees by itself with the interest earned every month. It's equivalent to withdraw $7 as the monthly interest, thus it's considered as simple interest.

The interest earned for a principal P in a given period t at a rate r is given by

$I=P\cdot r\cdot t$

The interest is assumed to cover the bank's fees, thus I=$7 for t= 1 month, thus, solving for r

$\displaystyle r=\frac{I}{P\cdot t}=\frac{7}{670\cdot 1}=0.0104$

The annual interest rate is

$r=0.0104*12=0.1254$

$\boxed{r=12.54\%}$