作业求助

linchan

Eight months ago, Louise agreed to pay Thelma $750 and $950, six and twelve
1 t6 n# t! P% N8 Ymonths respectively from the date of the agreement. With each payment, Louise
& k7 ~! @6 V5 p/ Y; Aagreed 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
6 h7 G! N( j( |: b5 ~7 X; ?2 ?; M) ]single payment four months from now. What payment should Thelma be willing to
& v3 z' R% b4 s' u/ x" |. w1 aaccept if money can earn 7.75%? （最好有过程）

littledognancy

Suppose Intr is annually compounded                                       
- f& R: t( U5 T                Month 0        Mon. 8                  Mon. 12
! ~6 m2 r3 V8 TCash Principal        X        -750                  -950       
8 {+ m. Y, U$ P0 g4 wCash 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]
" `! |# c! H6 g                                                 /(1+7.75%*8/12)           /(1+7.75%*12/12)
* F9 [3 |6 a) F- \+ g4 H1 p+ X# e
* L, G. W3 s7 w# Z& r7 Xthese 3 should add up to 0, i.e. NPV at month 0 is 0.
                                       
: [  E% `8 F& K  C3 K' HConclusion        X        =        1729.8               
& V# K4 X2 z/ e' K, R                                       
So, Initial borrowing was        1730        *(1+7.5%)        1859.5        approx.         $1,860

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