8. Niko bad his savings increase by \( 5 \% \) this year. He started with \( \$ 350 \) in his account and calculated how much he had at the end of the year by using the following sets of calculations: \[ \$ 350 \times 0.05=\$ 17.50 \quad \$ 350+\$ 17.50=\$ 367.50 \] Find a single number that Niko could have multiplied his starting amount of \( \$ 350 \) by to get \( \$ 367.50 \) by solving the equation below for \( r \). Why does this number make sense? \( 350 r=367.50 \)

To find the single number \( r \) that Niko could have multiplied his starting amount of \( \$ 350 \) to arrive at \( \$ 367.50 \), you can rearrange the equation \( 350r = 367.50 \) to solve for \( r \). Dividing both sides by \( 350 \) gives us: \[ r = \frac{367.50}{350} = 1.05. \] This number makes sense because \( 1.05 \) represents a \( 5\% \) increase over the original amount. When you multiply \( 350 \) by \( 1.05 \), you are effectively calculating \( 100\% + 5\% = 105\% \) of the original amount, thus confirming the \( 5\% \) increase in savings. Now, when you think about savings and interest, this concept is quite handy! By knowing how to calculate percentages in this way, you can easily assess your savings growth over time. Want to know more about calculating interest? Just remember, understanding simple and compound interest can significantly boost your financial literacy and help you make informed decisions about saving and investing!