作业求助

linchan

Eight months ago, Louise agreed to pay Thelma $750 and $950, six and twelve
3 @, Y& N2 l+ L7 s# F  W0 X( Gmonths respectively from the date of the agreement. With each payment, Louise
1 y1 t3 s! j! |4 [, a  S5 o' qagreed to pay interest at the rate of 9.5% pa from the date of the agreement. Louise
failed to make the first payment and now wishes to settle her obligations with a
/ z- A& U" U1 Asingle payment four months from now. What payment should Thelma be willing to
accept if money can earn 7.75%? （最好有过程）

littledognancy

Suppose Intr is annually compounded                                       
( X" t5 }7 f0 M# I                Month 0        Mon. 8                  Mon. 12
# p& f3 {% H' t1 U6 pCash Principal        X        -750                  -950       
Cash Intr (Should Pay)                -X*9.5%*8/12          -(X-750)*9.5%*4/12               
: ?, R" X/ t) n1 ^PV at mon 0        X        -[750+X*9.5%*8/12]          -[950+(X-750)*9.5%*4/12]
                                                 /(1+7.75%*8/12)           /(1+7.75%*12/12)

these 3 should add up to 0, i.e. NPV at month 0 is 0.
                                       
  U6 F' A, a6 z9 P5 U$ K! L+ \: pConclusion        X        =        1729.8               
2 w" U, f  \% x$ {$ [$ p; f7 P                                       
5 E; R2 ]  _' s+ _' q5 B6 g$ USo, Initial borrowing was        1730        *(1+7.5%)        1859.5        approx.         $1,860
# H4 ?$ \5 [* E" B

littledognancy

Finance 学得不好所以不知道做得对不对。。。看着办吧~ 也许有用。

linchan

对了，答案是$1856.32