Confusing IB Maths HL problem

Question

On the day of her birth, 1st January 1998, Mary's grandparents invested $x in a savings account. They continued to deposit $x on the first day of each month thereafter. The account paid a fixed rate of 0.4% interest per month. The interest was calculated on the last day of each month and added to the account.

As soon as Mary was 18 she decided to invest $15,000 of this money in an account of the same type earning 0.4% interest per month. She withdraws $1000 every year on her birthday to buy herself a present. Determine how long it will take until there is no money in the account.

Answer 1

you need excel for this question and the table should look like this.

 

 

year amount at the beginning of the year amount at the end of the year
1 $15,000.00 $15,060.11
2 $14,060.11 $14,116.45
3 $13,116.45 $13,169.02
4 $12,169.02 $12,217.78
5 $11,217.78 $11,262.73
6 $10,262.73 $10,303.86
7 $9,303.86 $9,341.14
8 $8,341.14 $8,374.57
9 $7,374.57 $7,404.12
10 $6,404.12 $6,429.79
11 $5,429.79 $5,451.55
12 $4,451.55 $4,469.38
13 $3,469.38 $3,483.29
14 $2,483.29 $2,493.24
15 $1,493.24 $1,499.22
16 $499.22 $501.22
17 $0.00 $0.00