;;; 4.11b2.scm
;;; 2016-04-02

(use gauche.sequence) ; for 'map-with-index' procedure

(define (main args)
; initialize and input
  (define x '(-40 10  10  10  10  10  10 )) ; cash flow stream
  (define s '(  0 5.0 5.3 5.6 5.8 6.0 6.1)) ; spot rate
  (define f  '())                           ; forward rate
  (define d  '())                           ; discount factor
  (define (p k x d)	; recursive procedure
    (if (= k (- (length x) 1))
      (ref x k)
      (+ (ref x k) (* (ref d (+ k 1)) (p (+ k 1) x d)))
    )
  )
  (define fmt "")
  (define (fix x n) (/ (round (* x (expt 10 n))) (expt 10 n)))

; calculate
  (set! s (map (lambda (x) (/ x 100)) s))
  (set! f (map-with-index
            (lambda (i x) 
              (cond ((= i 0) 0)
                    (else (- (/ (expt (+ 1 (ref s i)) i) 
                                (expt (+ 1 (ref s (- i 1))) (- i 1)) ) 
                             1)
                    )
              )
            )
            s
          )
  )
  (set! d (map (lambda (x) (/ (+ 1 x))) f))

;output
  (print "4.11b2.scm")
  (print "input")
  (format #t "~10a ~10a ~10a ~10a ~10a\n" 
             "k" "x[k]" "s[k]" "f[k-1,k]" "d[k-1,k]" )
  (print "----------" "----------" "----------" "----------" "----------")
  (for-each (lambda (i j k l m)
              (format #t "~10a ~10a ~10a ~10a ~10a\n"
               i j (fix k 3) (fix l 3) (fix m 3)))
            (iota 7) x s f d)
  (print "----------" "----------" "----------" "----------" "----------")
  (print "output")
  (print "pv= "  (fix (p 0 x d) 3) " (by running present value)")
0)
;;; end