;;;; Mortgage Calculators

#|
Formulas:

P = payment
PV = Present Value
r = rate per period
n = number of periods

Find payments
P = (r(PV)) / (1-(1+r)^-n)

Find total
P = (r(PV)) / (1-(1+r)^-n)
P * (1-(1+r)^-n) = r * PV
(P * (1-(1+r)^-n) / r = PV

Find rate
TODO

Find payments
TODO

|#

(defun find-payments (loan-total rate number-of-payments)
  "Generic payment calculation"
  (/ (* rate loan-total)
	 (- 1 (expt (+ 1 rate) (* number-of-payments -1)))))

(defun find-monthly-payments(loan-total rate number-of-payments)
  "Monthly payment by loan/rate/number of years"
  (find-payments loan-total (/ rate 12) (* number-of-payments 12)))

(defun find-monthly-payment-total-per-year (loan-total rate number-of-payments)
  "Total monthly payments per year"
  (* (find-monthly-payments loan-total rate number-of-payments) 12))


;; fixme: add function to take monthly-payments rate num-of-payments
(defun find-biggest-loan (payments rate number-of-payments)
  "Generic loan calculation"
  (/ (* payments
	   (- 1
		  (expt (+ 1 rate) (* -1 number-of-payments))))
	 rate))

(defun find-biggest-loan-monthly (payments rate number-of-payments)
  "Largest loan by payments/interest rate/number of years"
  (find-biggest-loan payments (/ rate 12) (* number-of-payments 12)))