College Algebra Word Problem

Question

If you borrow $4700 at an APR of r (as a decimal) from a lending institution that compounds interest continuously, and if you wish to pay off the note in 3 years, then your monthly payment M, in dollars, can be calculated using
M =
4700(er/12 − 1)
1 − e−3r
.
Your budget will allow a payment of $150 per month, and you are shopping for an interest rate that will give a payment of this size. What interest rate do you need to find? (Round your answer to two decimal places.)

Answer 1

 

Due to time constraints I had to solve this one numerically.

 

The max interest rate is  9.21173% but that is subject to round-off error

Anything less than 9.2% is safe

 

I got $150 payment correct to 4 decimal places doing this:

 

  4700*(exp(9.21173%/12 )- 1)

------------------------------------ 

  1 - exp(-3*9.21173%)

 

Note that when using your calculator, you MUST divide the percent by 100.

That is you input the percentage into your calculator is 0.0921173