Question

Write a formula that describes the value of an initial investment of $4000 that loses value at a rate of 10% per year, compounded six times per year.​

Answer 1

since the investment is losing 10%, let's plug that in the compound interest equation but with a negative rate of 10%.

`~~~~~~ \underset{\textit{with a negatie rate}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1~~ - ~~(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 10\%\to (10)/(100)\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{six times} \end{array}\dotfill &6\\ t=years\dotfill &t \end{cases}`

`A=4000\left(1~~ - ~~(0.10)/(6)\right)^(6\cdot t)\implies A=4000\left( (59)/(60) \right)^(6t)`