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Sample Question: If the present value of an annuity due of $400 payable semi-annually is $5600 and interest is compounded at 6% compounded semi-annually, what is the number of payments?
Solution: We need to find n such that
\[5600=\frac{400}{1.03}+\frac{400}{{{1.03}^{2}}}+...+\frac{400}{{{1.03}^{n}}}\,\,\,\Rightarrow \,\,\,\,14=\sum\limits_{i=1}^{n}{\frac{1}{{{1.03}^{i}}}}=\frac{0.970874-{{0.970874}^{n}}}{1-0.970874}\]
\[\Rightarrow {{0.970874}^{n}}=0.533107\,\,\Rightarrow \,\,\,n=19.42859\approx 19\]