Question

Raymond invested $4, 000 in a new company. The value of his investment has been growing at a rate of 6% per year for the last 5 vears. Write a function to represent the growth of his investment of $4,000, where A is the total value of his investment and t is the time invested in years. What is the total value of his investment after 5 years?

Answer 1

`~~~~~~ \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 6\%\to (6)/(100)\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=4000\left(1+(0.06)/(1)\right)^(1\cdot 5) \implies A=4000(1.06)^5\implies A \approx 5352.90`

now, we're assuming is a 6% growth of the current amount per year, namely compounded, as opposed to simple interest.