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
agreed to pay interest at the rate of 9.5% pa from the date of the agreement. Louise
( Q9 \: ~4 X! J8 o% nfailed 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                                       
6 B) Q4 y5 g/ }2 Q0 @" E# B                Month 0        Mon. 8                  Mon. 12
) j2 \, V( k: }8 M1 |' e0 s# {Cash Principal        X        -750                  -950       
Cash Intr (Should Pay)                -X*9.5%*8/12          -(X-750)*9.5%*4/12               
$ ~3 C( S# t, ~; [$ r- iPV at mon 0        X        -[750+X*9.5%*8/12]          -[950+(X-750)*9.5%*4/12]
6 _  O8 P/ P( ~                                                 /(1+7.75%*8/12)           /(1+7.75%*12/12)
1 m3 c" a( u/ z: t+ }1 @: h9 b* N
% X4 Z# P0 u, V, u& q, k1 M8 fthese 3 should add up to 0, i.e. NPV at month 0 is 0.
                                       
Conclusion        X        =        1729.8               
                                       
So, Initial borrowing was        1730        *(1+7.5%)        1859.5        approx.         $1,860
  g* b* b' I+ z0 y

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