Answer-
She saved $30 monthly.
Solution-
We know that,
[tex]\text{FV of annuity}=P[\frac{(1+r)^n-1}{r}][/tex]
Where,
P = periodic payment
r = rate per period
n = number of period
Here,
[tex]FV\ of\ annuity=\$6936.72,\\\\P=?,\\\\r = 5.75\%\ annually=\frac{5.75}{12}\%\ monthly=\frac{5.75}{1200}\ monthly\\\\n=13\ years=13\times 12=156\ months[/tex]
Putting the values,
[tex]\Rightarrow 6936.72=P[\dfrac{(1+\frac{5.75}{1200})^{156}-1}{{\frac{5.75}{1200}}}]\\\\\\\Rightarrow P=\dfrac{6936.72}{[\frac{(1+\frac{5.75}{1200})^{156}-1}{{\frac{5.75}{1200}}}]}\\\\\\\Rightarrow P=\dfrac{6936.72}{\frac{2.107947-1}{0.004792}}\\\\\\\Rightarrow P=\dfrac{6936.72}{\frac{1.107947}{0.004792}}\\\\\\\Rightarrow P=30[/tex]
Therefore, she saved $30 monthly.
