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Suppose Intr is annually compounded
+ @; b: C6 N) {# B# T; ~ Month 0 Mon. 8 Mon. 12! F, b9 I5 h$ K/ [' r: \9 ?$ X8 {% }
Cash Principal X -750 -950
. h1 g7 o4 U& K( FCash Intr (Should Pay) -X*9.5%*8/12 -(X-750)*9.5%*4/12 / c* @! Z; v8 T) }; p$ E
PV at mon 0 X -[750+X*9.5%*8/12] -[950+(X-750)*9.5%*4/12]
& s; z1 p/ c( i /(1+7.75%*8/12) /(1+7.75%*12/12)
1 U& P+ l: |/ C( c! W7 x6 b. S* w# Y7 {8 t
these 3 should add up to 0, i.e. NPV at month 0 is 0." M( l- t& r7 H: j
5 q; h% K8 C; i; EConclusion X = 1729.8
% p2 h9 w3 X, X ! R' M4 a. a# v* V2 u, u
So, Initial borrowing was 1730 *(1+7.5%) 1859.5 approx. $1,860
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