Question

On January 1, 2010, Joline deposits $1000 in a bank account that does not earn interest. For the next 12 months she deposits $25 each month. Then she withdraws $25 each month for the next 12 months. On January 1, 2010, Sofia deposits $1100 in an account that earns 0.25% interest each month.

a. Write two models: one for the amount in Joline's account and one for the amount in Sophia's account. State what the variables in your models represent.

b. In what months and years do the accounts have approximately the same amount, and what are the amounts?​

Answer 1

$1000 + $25m and $1300 - 25m ;

1100 + 2.75m

2010 (4th month)

2011 ( 7th month)

Explanation:

Joline's account :

Initial deposit = $1000

Monthly deposit = $25

Monthly withdrawal = $25

Number of months = 12

Let m = number of month at any point in time

Initial deposit + total deposit

Amount in Joline's account ; first 12 months

$1000 + $25m - - - (1)

Next 12 months :

$1000 + $25 *12 - 25m

1300 - 25m

Sofia's account :

Deposit amount = $1100

Interest per month = 0.25% = 0.0025

1100 + (1100 * 0.0025 * m)

1100 + 2.75m - - (2)

To find the month:

Equate equation 1 and 2, then find m

$1000 + $25m = 1100 + (1100*0.0025*m)

1000 + 25m = 1100 + 2.75m

25m - 2.75m = 1100 - 1000

22.25m = 100

m = 100 / 22.25

m = 4.494

In year 2010, they have approximately the same amount in the fourth month

1300 - 25m = 1100 + 2.75m

1300 - 1100 = 2.75m + 25m

200 = 27.75m

m = 200 / 27.75

m = 7.207

In 2011 ; they have approximately the se amount in the 7th month