Payment Monthly

[Guest]

A loan of $2700 is given for 3 yrs., with an interest rate of 13.86%. Determine monthly pmt.

Formula;

M = P /[ 1 - (1 + i)^-n / i]

M = monthly pmt.
P = total amt. of loan.
n = number of pmts.
i = rate of interest.


M = 2700 / [1 - (1 + .1386)^ -36 / .1386]

M = 2700 / [1 - (1.1386)^ -36 / .1386]

Not sure how to continue.

[Baltuilhe]

Good afternoon and Merry Christmas!

First of all, interest rate:
[tex](1+i_m)^{12}=1+i_a[/tex]

[tex](1+i_m)^{12}=1+13,86\%[/tex]

[tex]1+i_m=(1+13,86\%)^{1/12}[/tex]

[tex]i_m=(1+13,86\%)^{1/12}-1[/tex]

[tex]i_m\approx 1,087533092\%p.m.[/tex]

Now, the Ammount:
[tex]PV=PMT\cdot\left[\dfrac{1-\left(1+i_m\right)^{-n}}{i_m}\right][/tex]

[tex]2\,700=PMT\cdot\left[\dfrac{1-\left(1+i_m\right)^{-12\cdot 3}}{i_m}\right]=PMT\cdot\left\{\dfrac{1-{\underbrace{\left[\left(1+i_m\right)^{12}\right]}_{1+i_a}}^{-3}}{i_m}\right\}[/tex][/tex]

[tex]2\,700=PMT\cdot\left[\dfrac{1-\left(1+i_a\right)^{-3}}{i_m}\right][/tex]

[tex]PMT=\dfrac{2\,700\cdot i_m}{1-\left(1+i_a\right)^{-3}}[/tex]

[tex]PMT\approx 91,04[/tex]