Question 1069261
I agree that with
{{{y}}}= final balance,
{{{a}}}= amount initially deposited/invested,
{{{n}}}= annual yield (as a decimal),
{{{t}}}=  number of years,
the relationship between those variables is
{{{y=a*(1+n)^t}}} or {{{a=y/(1+n)^t}}} .
 
In this case, {{{n=0.075}}} because the yield per year is
{{{"7.5%"=7.5/100=0.075}}} 
All you have to do is substitute the values for {{{y}}} , {{{n}}} , and {{{t}}} :
a ={{{"$10,000"/(1+0.075)^13}}}={{{"$10,000"/1.075^13}}}={{{"$10,000"/2.560413069=highlight("$3,905.62")}}} 
NOTE: The values {{{2.560413069}}} and {{{"$3,905.62"}}} are rounded,
and I used help from the computer to calculate the final result,
with the computer doing its best to calculate {{{2.560413069}}} and {{{3905.62}}} accurately,
and properly rounding the results for display purposes.