Posted by Pamela on Friday, July 31, 2009 at 1:13am.
The posted expression for the monthly payment has missing parentheses. Perhaps that's why there are difficulties with getting the answer.
When transposing a complicated fraction to a single line, as you have done above, it is important to provide parentheses to delimit the numerator (which was done above) and the denominator (parentheses missing). In fact, the expression above has an embedded denominator which also requires parentheses.
If the expression is not transcribed correctly to a single line, it usually means that the operations will not be executed according to the proper priorities, and will result in incorrect answers.
Let's start with putting the expression straight, using the given notations
Let
A=Amount borrowed.
P=Monthly payment
m=number of payments
r="annual" interest (as advertised)
w=monthly interest, compounded monthly.
then
w=r/12
(The denominators are enclosed in square brackets)
P(A,w,m)=(Aw)/[1-1/[(1+w)^m]]
Note that this formula will be indefinite if the rate of interest is zero, in which case the payment is simply
P=A/m
Also, this formula assumes that the interest is compounded monthly, which increases the advertised 6% interest to 6.16778%.
Given numerical data for Alice:
A=25000
r=0.06
m=5*12=60
(a) The numerical value of w is as given by the formula, w=r/12=0.06/12=0.005
(b) the monthly payment P is given by
P(A,w,m)
=P(25000,0.005,60)
=(25000*0.005)/(1-1/(1.005^60))
=(125)/(1-1/(1.348850152549304))
=(125)/(1-0.74137219624435)
=(125)/(0.25862780375565)
=483.320038235716
=$483.32
(c) The total amount Alice would have paid after 60 months is 60*$483.32=$28999.20