Question

Greta is opening a savings account. She starts with $100 and plans to add $50 each week. What is the unit rate of change for this situation? Write an equation Greta can use to calculate the amount of money she will have after any number of weeks. How much money will she have after 1 year?

Answer 1

Greta starts with $100 in her savings account

She adds $50 each week

Balance after week 1 = 100 + 50 = 150

Part A

Unit rate of change here is = $\frac{\text{Balance after week 1 - Initial balance}}{\text{Initial balance}} * 100$

⇒ Unit rate of change here is = $\frac{\text{150 - 100}}{\text{100}} * 100$

⇒ Unit rate of change here is = 50%

Part B

Equation to calculate the amount of money Greta will have after any number of weeks = ?

Money after 'x' number of weeks = $\text{Initial Deposit + x * Weekly Deposit}$

⇒ Money after 'x' number of weeks = $\text{100 + x * 50}$

Part C

Money Greta will have after 1 year= ?

In a year there are 52 weeks

So, putting x = 52 in the solution of Part B

⇒ Money after 52 weeks = $\text{100 + 52 * 50}$

⇒ Money after 52 weeks = $\text{100 + 2,600}$

⇒ Money after 52 weeks = 2,700