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", "advice": "You are asked to find the present value of a deferred annuity (since the payments start after some time periods). Therefore we will use the present value of a deferred annuity formula
\n$\\displaystyle P=\\frac{1}{(1+i)^{k-1}}\\frac{C}{i}\\left(1-\\frac{1}{(1+i)^n}\\right)$
\nwhere $P$ is the present value, $k$ is the number of time periods until the first cash flow, $C$ is the cash flow per period, $i$ is the interest rate per period, and $n$ is the number of periods.
\nIn our situation we have,
\n$k=\\var{k}$,
\n$C=\\var{C}$,
\n$i=\\frac{\\var{ipa}\\%}{\\var{period[1]}}=\\frac{\\var{ipadec}}{\\var{period[1]}}$, $i=\\var{ipa}\\%=\\var{ipadec}$,
\n$n=\\var{years}\\times \\var{period[1]}=\\var{n}$, $n=\\var{n}$,
\nand therefore we have
\n$\\displaystyle P=\\frac{1}{\\left(1+\\simplify[unitDenominator]{{ipadec}/{period[1]}}\\right)^{\\var{k}-1}}\\frac{\\var{C}}{\\left(\\simplify[unitDenominator]{{ipadec}/{period[1]}}\\right)}\\left(1-\\frac{1}{\\left(1+\\simplify[unitDenominator]{{ipadec}/{period[1]}}\\right)^\\var{n}}\\right)$
\nCalculating this we find
\n$\\begin{align}P&\\approx \\var{P}\\\\&=\\$\\var{Prounded}\\quad \\text{(to the nearest cent)}\\end{align}$
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\n\n$\\$$ [[0]] (to the nearest cent)
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