Expert: Paul Klarreich - 10/6/2006

Question
My name is Byron and I am studying Finance right now.  I am confused as to what formulas to use in order to figure out the particular word problem on the bottom of this email.  I have already figured out her monthly payment and am now trying to figure out the interest difference.  Here is the problem, can you help me figure out what formula to use?

Loraine borrowed $12500 over four years for a car.   She paid monthly payments over that time and was charged 8.4% compounded monthly.  How much interest did she pay in the first half of the loan?  (first two years)  How much more was this than what she paid in the last two years?  

Answer
Byron Asks in Category Calculus ...
 
Subject:  Finance related
Private:  no
 
Question:  My name is Byron and I am studying Finance right now.  I am confused as to what formulas to use in order to figure out the particular word problem on the bottom of this email.  I have already figured out her monthly payment and am now trying to figure out the interest difference.  Here is the problem, can you help me figure out what formula to use?

Loraine borrowed $12500 over four years for a car.   She paid monthly payments over that time and was charged 8.4% compounded monthly.  How much interest did she pay in the first half of the loan? (first two years)  How much more was this than what she paid in the last two years?   

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Hi, Byron,
I am sure the salesmen have formulas to do this, but I think you could approach the problem this way:

At the start, you had a Mortgage with a term of four years and interest rate 8.4%, and you said you computed the payment.  There are formulas that relate:

Principal Amount  (12500 originally)
Interest rate     (8.4%)
Term              (four years, or 48 months)
Monthly payment   (computed from those)

From any three of these, you can compute the fourth.

Now look at the situation after two years -- the first half of the loan.  We will have:

Principal Amount  (we don't know)
Interest rate     (still 8.4%)
Term              (now TWO years, or 24 months)
Monthly payment   (same as before)

This is now a TWO year mortgage, with known interest rate, term, and payment, from which we can compute the CURRENT PRINCIPAL.  

Once you have that, you can probably figure out the rest of the numbers.