Expert: Josh - 2/14/2007

Question
If I wanted to buy a $45,000.00 car and I put down a 10% depost.Borrow the rest at a 3% interest compounded monthly for 4 years.
1.What are my monthly payments?
2.When I am done paying for the car how much did I spend on interest?
Please show me step by step the answer.
Thanks Lily  

Answer
Dear Lily,

The amount of money you borrow is 90% of $45k, i.e., $40500.00

The formula for your monthly instalment is given by
M=[P*r*(1+r)^N]/[(1+r)^N-1]

I refer you to http://www.geocities.com/joshcameron_ae/Archive/Q0011.html for its derivation and detailed explanations. The symbols are also carefully described in that document. (Note: In general, the notation x^y means raise x to the power of y).

Important note: Here, I assume the 3% represents monthly (not annual) interest. In this case, interest rate r=0.03. If the quoted figure actually represents annual interest, you have to further divide "r" by 12.

P=40500, r=0.03, N=48 (months)
1) Monthly instalment, M=(P*r*(1+r)^N)/((1+r)^N-1)=$1602.89
2) Total interest paid is M*N-P=$36439.19 rounded to the nearest cent.

Comment: Check whether the 3% is interest per annum, or the monthly interest rate.

Regards,
J