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

I am not sure what formula to use... maybe d=r/1+rn
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2 Answers

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.