+0

# What would be the monthly payment for $20,000 at 6.9% financing for 60 months? 0 590 6 What would be the monthly payment for$20,000 at 6.9% financing for 60 months?

Guest Jul 2, 2014

#3
+93677
+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
+576
+5

$395.08 Answer found using a calculator at http://www.mortgagecalculator.org/ jboy314 Jul 2, 2014 #2 +90023 +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
+93677
+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
#4
+93677
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
+27052
+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
+93677
0

Thanks Alan.

Melody  Jul 3, 2014