Don contribute 200 at the end of each quarter to a Tax Sheltered Annuity (TSA). What will the value of the TSA be after the 80th deposit (20 years) if the per annum rate of return is assumed to be 7% compounded quarterly?
Solution:-
Suppose P is the deposit in dollars made at each payment period for an annuity paying i percent interest per payment period. The amount A of the annuity after n deposits is
A = ![P\frac{(1+i)^[n]-1}{i}](https://mymathangels.com/wp-content/ql-cache/quicklatex.com-4a650b849335a1afa7840b706ad9ded6_l3.png "Rendered by QuickLaTeX.com")
This is an annuity with P = 200, n = 80, and i = 
. The value of the TSA after the 80th deposit is given below.
A =![200[\frac{(1+\frac{0.07}{4})^{80}-1}{\frac{0.07}{4}}]](https://mymathangels.com/wp-content/ql-cache/quicklatex.com-0fcac150b69563fb73d3c25af1ce3222_l3.png "Rendered by QuickLaTeX.com")
A 
34358.76