Question

Question #a99bd

Answer 1

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`