Question

The annual interest rate on a $10,000 loan is 18%. The exponential function that represents this is y=10000(1.18t). Write the exponential function for this loan in terms of a monthly interest rate?

Answer 1

`\bf ~~~~~~ \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 &\$10000\\ r=rate\to 18\%\to (18)/(100)\dotfill &0.18\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years \end{cases} \\\\\\ A=10000\left(1+(0.18)/(12)\right)^(12\cdot t)\implies A=10000(1.015)^(12t)`

Answer 2

B) y = 10000(1.014)12t

Explanation: