What would be the monthly payment for $20,000 at 6.9% financing for 60 months?
that is interesting. I got the same answer but on the surface our forumulas look different.
$$\begin{array}{rll}
A&=&M \left(\dfrac{1-(1+i)^{-n}}{i}\right)\\\\
A\times \dfrac {i}{1-(1+i)^{-n}}&=&M\\\\
M&=&A\times \dfrac {i}{1-(1+i)^{-n}}\\\\
M&=&20000\times \dfrac {0.00575}{1-(1.00575)^{-60}}\\\\
M&\approx &\$ $395.08
\end{array}$$
Let's see how jboy314's answer was derived.
The "formula" for the monthly payment is given by:
M = P(1+r)n r / [(1+r)n-1]
Where
M = the Monthly Payment
P = the amount financed ($20000)
r = the montly interest rate expressed as a decimal = .069/12 = .00575
So we have
M = (20000*(1+.00575)^60*.00575)/ ((1+.00575)^60 -1)) = $395.08
that is interesting. I got the same answer but on the surface our forumulas look different.
$$\begin{array}{rll}
A&=&M \left(\dfrac{1-(1+i)^{-n}}{i}\right)\\\\
A\times \dfrac {i}{1-(1+i)^{-n}}&=&M\\\\
M&=&A\times \dfrac {i}{1-(1+i)^{-n}}\\\\
M&=&20000\times \dfrac {0.00575}{1-(1.00575)^{-60}}\\\\
M&\approx &\$ $395.08
\end{array}$$
There you go - I challange someone to do the mathas and show why the formulas are indeed the same.