Solver Find the Present Value for a Loan
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==section input You take out a *[input t=10] year loan for $*[input 8 cost=20000]. The APR is *[input apr=5]% and you put $*[input 6 down=2000] as a down payment. What is the monthly payment? ==section solution To find the monthly payment, we have to use this formula, {{{PV=R*(1-(1+r/k)^(-kt))/(r/k)}}}, where PV is the present value, R is the monthly payment, r is the APR, and k is the amount of payments you make per month, in this case it is 12. Plugging all the numbers in we get *[assign r=$apr/100] *[assign PV=$cost-$down] {{{$PV=R*(1-(1+$r/12)^(-12*$t))/($r/12)}}}. Simplifying the right side we get *[assign a=1+$r/12] *[assign b=-12*$t] *[assign c=$r/12] {{{R*(1-$a^$b)/$c}}} So we have that {{{R=$PV/((1-$a^$b)/$c)}}}. *[assign d=$a^$b] {{{R=$PV/((1-$d)/$c)}}} *[assign e=(1-$d)/$c] {{{R=$PV/$e}}} *[assign ans=$PV/$e] {{{highlight(highlight_green(highlight(R=$ans)))}}} So we have that the monthly payment is $$ans. ==section output r,PV,a,b,c,d,e,ans ==section check
