Big Ideas Math: Modeling Real Life, Grade 7
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Big Ideas Math: Modeling Real Life, Grade 7 View details
6. Simple Interest
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Exercise 17 Page 269

Use the simple interest formula I=Prt, where I is the interest, P the principal, r the annual interest rate, and t the time in years.

4%

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If we borrow money from a bank, we pay the bank interest for the use of their money. Similarly, if we open a savings account, the bank deposits extra money on this account as interest. To calculate the interest I, we use the simple interest formula. I= P r t, where... I& = Interest P& = Principal r& = Annual interest rate t& = Time (in years)We know that we deposit $\col{\$900}$ in a savings account with we earn $\colII{\$54}$ simple interest in $\colIII{18}$ months. We want to calculate the annual rate. Keep in mind that $18$ months represents $\colIII{\frac{18}{12}}$ years. \begin{gathered} \col{P}=\col{900}, \quad \colII{I}=\colII{54}, \quad \colIII{t}=\colIII{\dfrac{18}{12}} \end{gathered} To calculate the interest, we will substitute these values into the simple interest formula and solve the resulting equation for $r.$

\(I=Prt\)
\(\colII{54}=(\col{900})(\colV{r})\left(\colIII{\dfrac{18}{12}}\right)\)
\(54\t 12 = (900)(\colV{r})\left(\dfrac{18}{12}\right)\t 12\)
\(54\t 12 = (900)(\colV{r})(18)\)
\(\dfrac{54\t 12}{(900)(18)}=\dfrac{(900)(\colV{r})(18)}{(900)(18)}\)
\(\dfrac{54\t 12}{(900)(18)}=\dfrac{(\cancel{\colVI{900}})(\colV{r})(\cancel{\colIV{18}})}{(\cancel{\colVI{900}})(\cancel{\colIV{18}})}\)
\(\dfrac{54\t 12}{(900)(18)}=\colV{r}\)
\(\dfrac{648}{16\,200}=\colV{r}\)
\(0.04=\colV{r}\)
\(\colV{r}=0.04\)

Since the decimal number $0.04$ is equal to $4\%,$ the annual interest rate is $4\%.$