Question

How much more interest is owed on $900 for 9 months then for 6 months? 6 months = 2.4% rate 9 months = 2.9% rate

Answer 1

Keeping in mind that 6 months is not even a year, since there are 12 months in a year, then 6 months is really 6/12 years, and 9 months is 9/12 years, then


$\bf ~~~~~~ \textit{Simple Interest Earned on 9 months}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\to& \ 900\\ r=rate\to 2.9\%\to \frac{2.9}{100}\to &0.029\\ t=years\to \frac{9}{12}\to &\frac{3}{4} \end{cases} \\\\\\ I=900(0.029)\left( \frac{3}{4} \right)\\\\ -------------------------------$

$\bf ~~~~~~ \textit{Simple Interest Earned on 6 months}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\to& \ 900\\ r=rate\to 2.4\%\to \frac{2.4}{100}\to &0.024\\ t=years\to \frac{6}{12}\to &\frac{1}{2} \end{cases} \\\\\\ I=900(0.024)\left( \frac{1}{2}\right)$

check their difference, that much.