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\n\nSuppose {company} purchased a $\\var{full}$-day promissory note at a yield of $\\var{originalipa}\\%$ per annum. The promissory note had a face value of $\\$\\var{S}$. After holding the promissory note for $\\var{soldafter}$ days {company} sold the promissory note at a yield of $\\var{nextipa}\\%$ per annum.
", "extensions": [], "advice": "a)
\nWe are asked to find the present value of a promissory note. We do this using simple interest. Therefore we will use the equation
\n$\\displaystyle P=\\frac{S}{(1+rt)}$,
\nwhere $P$ is the present value, $S$ is the future value (the face value, or the value at maturity), $r$ is the interest rate (or the yield) per annum and $t$ is the time in years.
\nIn our situation we have,
\n$S=\\var{S}$,
\n$r=\\var{originalipa}\\%=\\var{originalipadec}$,
\n$t=\\frac{\\var{full}}{365}$,
\nand therefore
\n$\\begin{align}P&=\\frac{\\var{S}}{1+\\var{originalipadec}\\times \\frac{\\var{full}}{365}}\\\\&=\\$ \\var{aProunded} \\text{ (to the nearest cent)}\\end{align}$
\n\nb)
\nWe are asked to find the present value of a promissory note. We do this using simple interest. Therefore we will use the equation
\n$\\displaystyle P=\\frac{S}{(1+rt)}$,
\nwhere $P$ is the present value, $S$ is the future value (the face value, or the value at maturity), $r$ is the interest rate (or the yield) per annum and $t$ is the time in years.
\nIn our situation we have,
\n$S=\\var{S}$,
\n$r=\\var{nextipa}\\%=\\var{nextipadec}$,
\n$t=\\frac{\\var{left}}{365}$, (since $\\var{full}-\\var{soldafter}=\\var{left}$)
\nand therefore
\n$\\begin{align}P&=\\frac{\\var{S}}{1+\\var{nextipadec}\\times \\frac{\\var{left}}{365}}\\\\&=\\$ \\var{bProunded} \\text{ (to the nearest cent)}\\end{align}$
\n\nc)
\nSince {company} purchased the promissory note for $\\$\\var{aProunded}$ and sold it for $\\$\\var{bProunded}$ the dollar return was $\\$\\var{bProunded}-\\$\\var{aProunded}=\\$\\var{c}$
\n\nd)
\nWe are asked to find the interest rate using simple interest. Therefore we could use the equation
\n$I=Ptr$,
\nwhere $I$ is the interest amount, $P$ is the present value, $t$ is the time in years and $r$ is the interest rate per annum.
\n\n\nIn our situation we have,
\n$I=\\var{c}$,
\n$P=\\var{aProunded}$,
\n$t=\\frac{\\var{soldafter}}{365}$,
\nand therefore we have
\n$\\displaystyle \\var{c}=\\var{aProunded}\\times \\frac{\\var{soldafter}}{365}\\times r$
\nwhich we need to rearrange to solve for $r$.
\n\nWe want to get $r$ by itself. We can do this by dividing both sides by $\\var{aProunded}\\times \\frac{\\var{soldafter}}{365}$ (in order to remove the multiplication by $\\var{aProunded}\\times \\frac{\\var{soldafter}}{365}$)
\n$\\displaystyle \\frac{\\var{c}}{\\var{aProunded}\\times \\frac{\\var{soldafter}}{365}}=r$
\nCalculating this we find
\n$\\begin{align}r&\\approx\\var{ddec}\\\\&=\\var{drounded}\\%\\text{ (to 2 decimal places)}\\end{align}$
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", "group": "Ungrouped variables", "definition": "365*c/(aP*soldafter)"}, "originalipa": {"templateType": "anything", "name": "originalipa", "description": "interest per annum as a percentage (add the symbol afterwards)
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