Question

Katie needed to take out three loans. a) First, she paid $596.24 in interest on a nine-month loan for which the rate was 11%. How much money did she borrow? b) A year later, Katie borrowed $10,000 for three months. If she paid $225 in interest, what rate of interest did she pay? c) Finally, Katie borrowed $12,000 at 10% interest. If she paid $600 in interest, for how long was the loan?

Answer 1

now.. for a) and b) parts

keep in mind for the equation " i = Prt " the "t" stand for years
a) has 9months, 9 months from 12 months is 3/4 of a year
b) has 3 months, and that's just 1/4 of a year

a)


`\bf \qquad \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\to &\$596.24\\ P=\textit{original amount}\\ r=rate\to 11\%\to (11)/(100)\to &0.11\\ t=years\to &(3)/(4) \end{cases} \\\\\\ 596.24=P\cdot 0.11\cdot \cfrac{3}{4}`

solve for P

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b)


`\bf \qquad \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\to &\$225\\ P=\textit{original amount}\to &\$10000\\ r=rate\\ t=years\to &(1)/(4) \end{cases} \\\\\\ 225=10000\cdot r\cdot \cfrac{1}{4}`

solve for "r"
now, you'd get a decimal amount, as you notice in the first one, rate in % is just whatever/100, so, to get the % figure, simply multiply it by 100



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c)


`\bf \qquad \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\to &\$600\\ P=\textit{original amount}\to &\$12000\\ r=rate\to 10\%\to (10)/(100)\to &0.1\\ t=years \end{cases} \\\\\\ 600=12000\cdot 0.1\cdot t`

solve for "t"