Problem 600


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?




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}


This is an annuity with P = 200, n = 80, and i = \frac{0.07}{4}. 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}}]


A \approx 34358.76

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