Question

You guys I need help with something like this again

Answer 1

In general an annual rate of $r$ compounded monthly will multiply the amount by a factor of $1+\frac{r}{12}$ each month. 

Each month of 4.3% is a factor of  $1+\frac{.043}{12}$.  That goes for five months, so is multiplied by itself five times, so gets a fifth power.

Each month of 13.7% is a factor of $1+\frac{.137}{12}$.  He pays this for 12-5=7 months, so it gets an exponent of seven.

We started the year owing $2600 of principal, so after the year we owe

$2600(1+\frac{.043}{12})^5(1+\frac{.137}{12})^7$.

Choice A.