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
2 e0 \( I1 n/ m$ @agreed 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
4 v- [% [& Q# e/ P' `8 dsingle payment four months from now. What payment should Thelma be willing to
; ^6 b# E. f: l1 ~; P8 `accept if money can earn 7.75%? （最好有过程）

littledognancy

Suppose Intr is annually compounded                                       
+ }6 o/ s" O& _* k. K; X                Month 0        Mon. 8                  Mon. 12
Cash Principal        X        -750                  -950       
0 n8 P+ I- D* A- X) ~; H7 |& tCash 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]
                                                 /(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.
9 i+ Z, x# w1 `0 }- ]1 K' q                                       
7 z3 Q& a" Z+ |+ k2 ]Conclusion        X        =        1729.8               
* R  b, P# h7 S8 l4 {8 q                                       
3 x7 t7 v& i  p, O5 I: S! a. `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