Question

you buy a car for 44,000 it depreciates at a rate of 3 percent semi annually how much is it after 4 years

Answer 1

let's say the car is "appreciating with a negative rate" of 3%, which is the same as depreciating at a rate of 3%, so in essence let's use the compound interest formula with a negative rate of 3%.

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{depreciated amount}\\ P=\textit{original amount deposited}\dotfill &\$44000\\ r=rate\to -3\%\to (-3)/(100)\dotfill &-0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases}`

`A = 44000\left(1+(-0.03)/(2)\right)^(2\cdot 4) \implies A = 44000( 0.985)^(8)\implies A \approx 38989.04`