MY QUESTION IS IF WE BEGIN IN 2007 &1993 INSTEAD OF 1998 & 1993, HOW THE PURCHASED COST WILL DIFFER

Ps: this is the solution in 1998 &1993 i want different solution (the question is in pic. )

Apply the power rule,

Vessel (75m^3 )cost in 1993 / Vessel (155m^3) cost in 1993

= 7800*1.4 / C2 = [Capacity of vessel in1993/capacity of vessel in 1998]^n

C2 = 10920*(155/75)^n ........................(1)

Apply the cost index formula,

Present cost = original cost (index value present time/index value at time cost was obtained)

13800*1.65 = (10920*(155/75)^n)*(390/359)

or, 1.91942 = (155/75)^n.........(2)

taking log of equation(2),

n = ln(1.91942)/ln(155/75) = 0.8981

Hence,

present cost (year 2007) $ = (13800*1.65*(120/155)^0.8981)*Cost index of 2007/cost index of 1998

$ = (582/390)*(13800*1.65*(120/155)^0.8981)

$= 27002.08

Date 1993 1998 2007 Vessel Capacity (m) 75 155 120 Purchased Cost (Pounds Sterling = ) 7,800 13,800 Exchange Rate $1.40/ $1.65/ $2.00/