We have to calculate an annuity with the following characteristics:
• Payment amount: $ 135 (M = 135)
• Subperiod: quarterly (number of subperiods, n = 4)
,
• Interest rate: 4% (r = 0.04)
,
• Period: 4 years (t = 4)
We can now use the formula for the future value (A), as they willl withdraw the money after the 14 years:
[tex]A=M*\frac{(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}}[/tex]
We can replace the variables with its values and find A:
[tex]\begin{gathered} A=135*\frac{(1+\frac{0.04}{4})^{4*14}-1}{\frac{0.04}{4}} \\ A=135*\frac{(1.01)^{56}-1}{0.01} \\ A=135*\frac{1.74580981920691451592-1}{0.01} \\ A=135*\frac{0.74580981920691451592}{0.01} \\ A=135*74.850981920691451592 \\ A\approx10068.43 \end{gathered}[/tex]
Answer: the future value of the annuity is $10,068.43.
