What would be the monthly payment for $20,000 at 6.9% financing for 60 months?

Guest Jul 2, 2014

#3**+8 **

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}$$

Melody
Jul 3, 2014

#1

#2**+8 **

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

CPhill
Jul 2, 2014

#3**+8 **

Best Answer

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}$$

Melody
Jul 3, 2014

#4**0 **

There you go - I challange someone to do the mathas and show why the formulas are indeed the same.

Melody
Jul 3, 2014