It is useful to work out how the period of a bond repayment changes if you increase or decrease P$.$ The formula for N is given by$,$

$($a$)$ Write a new program to compute this formula. Use the built$-$in function log for the natural logarithm ln$.$ How long will it take to pay off a loan of $$50,000$ at $$800$ a month if the interest remains at $15\%?$

$($b$)$ Use your program to find out by trial and error the smallest monthly payment that will pay off the loan this side of eternity.

Hint: recall that it is not possible to find the logarithm of a negative number, so P must not be less than

For part $($b$)$ write down the answer as a comment in the MATLAB script