Question

You deposit 365.00 into a savings account. After one year, the amount in the account is 428.00. Which expression describes the percent of increase in the account balance

Answer 1

the amount in increase is .... well 428 - 365 = 63.

if we take 365 to be the 100%, what is 63 off of it in percentage?

`\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 365&100\\ 63&x \end{array}\implies \cfrac{365}{63}=\cfrac{100}{x}\implies 365x=6300 \implies x = \cfrac{6300}{365} \\\\\\ x = \cfrac{1260}{73}\implies x = 17(19)/(73)\implies x \approx 17.26`

Answer 2

The expression that describes the percent of increase in the account balance is r = 428/365 - 1

Explanation:

1. Let's review the information provided to us to understand better the question and how to solve it.

Initial deposit into a savings account = US$ 365

Final amount = US$ 428

Time = 1 year simple interest because there it's not compounded during this term

2. Which expression describes the percent of increase in the account balance?

Let's recall the formula of the simple interest:

Final amount = Initial deposit * (1 + r * t)

Replacing with the real values, we have:

428 = 365 * (1 + r), given that t = 1 because the time is one year

428/365 = (1 + r)

428/365 - 1 = r

r = 1.173 - 1

r = 0.173 (rounding to two decimal places)

The expression that describes the percent of increase in the account balance is r = 428/365 - 1 and r = 0.173 is the expression that solve for r