Question

You place $4,000.00 in a bank account with an interest rate of 5.25% APR and another $2,000.00 in an account with an interest rate of 6.00% APR. Which account has your money working for you the best?

Answer 1

The correct answer is:

The $4000 with an APR of 5.25%.

Explanation:

While 6% APR is higher than 5.25%, it is only 0.75% higher (6.00-5.25 = 0.75).  This means that for every $100 invested, you would earn only $0.75 more with this interest rate.

We also are depositing twice as much money into the account with the slightly smaller APR.  

The equations to represent these situations are of the form $y=a*(1+r)^x$, where a is the principal invested, r is the interest rate expressed as a decimal number, and x is the number of years.  For the $2000, the equation would be

$y=2000(1+0.06)^x

\\

\\y=2000(1.06)^x$

For the $4000, the equation would be

$y=4000(1+0.0525)^x

\\

\\y=4000(1.0525)^x$

After 1 year, the $2000 would grow to $2120, earning $120 in interest.  The $4000, however, would grow to $4210, earning $210 in interest.

Each year, both accounts would grow by increasing amounts; however, the $4000 account will always earn more interest than the $2000 account.  The differences in the APR is too small to greatly affect this.