Question

You want to borrow $58,000 from your local bank to buy a new sailboat. You can afford to make monthly payments of $1,200, but no more.

Required:
Assume monthly compounding, what is the highest rate you can afford on a 60-month APR loan?

Answer 1

$58,000 = present value of 60 month monthly payments
let r be the monthly interest rate
$58,000 = 1200* (1/(1+r) + 1/(1+r)^2 + 1/(1+r)^3 +..... 1/(1+r)^60)
r = 0.738%

Answer 2

PV = 58000
n = 60 months
PMT = 1200

calculate i
this will give the monthly interest rate. (for max PMT of 1200, i will be maximum)

to convert monthly i into yearly i
we do (1+i)^12 - 1

As I am sure, you would appreciate the method/concept rather than the answer, I am not including the final answer

Please rate my solution!
Thanks in advance :)