Julie and Bill Stevens are purchasing a tractor and will need a $$200,000$ loan. The contractual rate is currently $5\%$ with $10$ equal annual payments. Their lender uses the add$-$on method of calculating interest.

a$.$ What are the annual payments?

b$.$ What is the effective interest rate of the loan?

c$.$ What is the effective total interest cost if the lender uses the remaining balance method $($constant payment method$)$ of calculating interest?

d$.$ Suppose Farm and Ranchers Bank and Trust uses the discount method of calculating interest.

i$.$ What are the annual payments?

ii$.$ What is the effective interest rate of the loan?

e$.$ What would be the effective interest rate of the loan if another bank requires to maintain $15\%$ of loan amount as a minimum balance in that loan account?