Question #a99bd

1 Answer
Feb 23, 2017

Answer:

After 4 years compounded depreciation at 50% the final value is
$2.38 rounded to 2 decimal places.

Explanation:

Depreciation (decay) is the opposite of appreciation (growth)

As in finance let the initial value (in finance it is the loan) be #P#
Let the number of calculation cycles be #n#
Let the percentage change be #x%->x/100#
Let value be at calculation n be #V_n#

#color(brown)("For growth:")#

Calculation 1
#V_1=P+x/100P" " =" " P(1+x/100)#

Calculation 2
#->V_2" "=" "P(1+x/100)(1+x/100)" " =" "P(1+x/100)^2#

Calculation #n#
#-> V_n= P(1+x/100)^n#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("For decay (depreciation):")#

#+x/100# increases it so logically #-x/100# decreases it. Thus we have:

#V_n=P(1-x/100)^n#

Substituting known values we have:

#V_4=$38(1-50/100)^4#

#V_4=$38(50/100)^4#

#V_4=$2.375#