作业求助

linchan

Eight months ago, Louise agreed to pay Thelma $750 and $950, six and twelve
6 `  i& W) ~& Z# `7 O2 L6 G1 nmonths respectively from the date of the agreement. With each payment, Louise
agreed to pay interest at the rate of 9.5% pa from the date of the agreement. Louise
0 }& X  g6 i/ y$ D2 k( _failed to make the first payment and now wishes to settle her obligations with a
$ I* w5 s: l0 h& U1 @single payment four months from now. What payment should Thelma be willing to
- S$ L! E; K5 J! b' x" m  Q/ Xaccept if money can earn 7.75%? （最好有过程）

littledognancy

Suppose Intr is annually compounded                                       
; ~/ U& ^( L1 b# r4 h: i- R                Month 0        Mon. 8                  Mon. 12
) T1 z  e& f- {Cash Principal        X        -750                  -950       
Cash Intr (Should Pay)                -X*9.5%*8/12          -(X-750)*9.5%*4/12               
PV at mon 0        X        -[750+X*9.5%*8/12]          -[950+(X-750)*9.5%*4/12]
  _. S/ G$ c4 [, x                                                 /(1+7.75%*8/12)           /(1+7.75%*12/12)
! a! O5 j8 y7 J# A- J/ v' I" S$ x
these 3 should add up to 0, i.e. NPV at month 0 is 0.
                                       
2 G6 i( k, k# b6 T3 C& L- nConclusion        X        =        1729.8               
9 N0 j  g8 \) {6 u8 r8 R! V+ n                                       
So, Initial borrowing was        1730        *(1+7.5%)        1859.5        approx.         $1,860
, c3 N3 {- ^9 h  L: X

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