For a term loan with initial principal $($total loan amount$)$ value of $P,$ the monthly payment A can be computed with the formula:

$A=\frac{iP(1+i{)}^n}{(1+i{)}^n-1}$

Where $i$ is the monthly interest rate $($decimal value$),$ computed from an annual rate $($decimal value not percent$)r$ as $i=\frac{r}{12},$ and $n$ is the number of months in the term of the loan.

Consider a $$100,000$ loan. Write a script that generates a $3-$column matrix of monthly payment options for terms of $5,10,$ and $20$ years respectively with rows corresponding to annual interest rates ranging from $4\mathrm{.}0\%$ t$6\mathrm{.}0\%$ in increments of $0\mathrm{.}125\%.$ Assign the matrix to a double precision variable named MonthlyPaymentTable.

Solve this problem using only vectorized code with no loops.