+0  
 
0
357
6
avatar

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

Guest Jul 2, 2014

Best Answer 

 #3
avatar+91451 
+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
Sort: 

6+0 Answers

 #1
avatar+576 
+5

$395.08

Answer found using a calculator at http://www.mortgagecalculator.org/

jboy314  Jul 2, 2014
 #2
avatar+81004 
+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
avatar+91451 
+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
avatar+91451 
0

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

Melody  Jul 3, 2014
 #5
avatar+26402 
+5

Just take the right-hand side of Chris's formula and divide top and bottom by (1+r)n.  

His equation becomes  M = Pr/(1-1/(1+r)n) or M = Pr/(1-(1+r)-n)

Replace his P by your A and his r by your i.  

Alan  Jul 3, 2014
 #6
avatar+91451 
0

Thanks Alan.

Melody  Jul 3, 2014

19 Online Users

avatar
avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details