作业求助

linchan

Eight months ago, Louise agreed to pay Thelma $750 and $950, six and twelve
months respectively from the date of the agreement. With each payment, Louise
8 M8 G1 t9 q9 s8 zagreed to pay interest at the rate of 9.5% pa from the date of the agreement. Louise
+ D% E. p$ l1 s( v0 Q7 ffailed to make the first payment and now wishes to settle her obligations with a
single 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                                       
$ J4 l- Z3 T4 u) E0 b6 ~" W                Month 0        Mon. 8                  Mon. 12
: m& i/ t2 J/ }" F2 iCash Principal        X        -750                  -950       
6 T5 j5 I3 b# p' _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]
& G" H: |/ S4 X  H/ s                                                 /(1+7.75%*8/12)           /(1+7.75%*12/12)
/ U/ H" [) b* w/ a' B+ p
7 K0 Y! ~+ I8 C5 H; l* \+ p5 W5 Tthese 3 should add up to 0, i.e. NPV at month 0 is 0.
2 h. b, ^  |/ ?* u  w& p: p                                       
Conclusion        X        =        1729.8               
8 Z* a8 \) [8 z" U                                       
- H8 b1 f  A" z: G! E# Z0 BSo, 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