Question

Dorothy Laymon is currently considering two bank card offers that are the same in all aspects except for the following. Bank A changes no annual fee and changes monthly interest 0f 1.57% on the unpaid balance. Bank B changes a$29 annual fee and monthly interest of 1.39% on the unpaid balance. From her records, Dorothy has found that the unpaid balance she tends to carry from month to month is quite consistent and averages $970.Estimate her total yearly cost to use the card if she chooses the card from Bank A and Bank B.

Answer 1

Bank A:

There are no annual fees, so we only need to consider the monthly interest.

The initial unpaid balance is $970; therefore,

`\begin{gathered} TotalCostA=_{}12\cdot970(0.0157)^{}=182.748 \\ \Rightarrow\text{TotalCostA}\approx182.75 \end{gathered}`

Where 0.0157=1.57% and the 12 in the exponent is there because of the 12 months that a year consists of. The answer is $182.75, bank A.

Bank B:

We need to do something similar to the previous step, the only changes are the interest rate and the annual fee; therefore,

`\begin{gathered} \text{TotalCostB}=29+12\cdot970(0.0139)^{}=190.796 \\ \Rightarrow\text{TotalCostB}\approx190.8 \end{gathered}`

The answer is $190.8, bank B