Question

Greta is opening a savings account. She starts with $100 and plans to add $50 each week. How do you write an equation she 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 will have `color(blue)($ 2,700` after one year in her savings account.

Explanation:

Initial deposit `a = $ 100`

Deposited after one week `d = $ 50`

Amount after one week `A^_1 = a + d = 100 + 50 = $ 150`

Amount after two weeks `A_2 = A_1 + d = (a + d) + d = a + 2d = 100 + (2 * 50) = $ 200`

Similarly after three weeks,

`A_3 = (a + 2d) + d = a + 3d`

Hence after n number of weeks,

`A_n = a + nd`

In a year, there are 52 weeks.

Thus after one year ( or 52 weeks),

`A_(52) = a + (52 * d) = 100 + (52 * 50) = 100 + 2600 =color(blue)( $ 2,700`