how long would it take to pay off a loan of $2,900 at 11% discount when the bank charges $638?

 

 

PV = 2900

I = .11

PMT = -638

FV = 0

 

You did not say how often the payments are being made. I am going to assume they are made once per year since $638 is a pretty heft payment to be making every month on a $2900 loan.

 

You can just enter the above variables into a TVM (time value of money) solver, or you can use a formula. The formula is quite messy however. Here is the formula for the present value of an annuity:

 

PV = PMT * [(1-(1+i)^-n) / i ]

 

Use algebra to rearrange to the following:

 

(1+i)^n =  1 / [1 - (PV / PMT)*i]

           

You can solve for n by applying the following property of logarithms:

 

ln [( 1+i)^n]= n[ln(1+i)]

 

n = ln ( 1 / [1 - (PV / PMT)*i] ) / ln (1+i)

 

I know this is extremely difficult to see and read given the font restrictions.