In general an annual rate of [tex]r[/tex] compounded monthly will multiply the amount by a factor of [tex]1+\frac{r}{12}[/tex] each month.
Each month of 4.3% is a factor of [tex]1+\frac{.043}{12}[/tex]. 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 [tex]1+\frac{.137}{12}[/tex]. 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
[tex]2600(1+\frac{.043}{12})^5(1+\frac{.137}{12})^7[/tex].
Choice A.
