Question

Alicia has invented a new app that two companies are interested in purchasing for a 2-year contract. Company A is offering $10,000 for the first month and will increase the amount each following month by $5000. Company B is offering $500 for the first month and will double their payment each following month. For which monthly payment will Company B's payment first exceed Company A's payment?

Answer 1

Month 8

In this month Company B's plan will pay $64,000 versus $45,000 from Company A.

Explanation:

Start by calculating the monthly payments for both plans.

Month - Company A - Company B

1 $10,000 $500

2 $15,000 $1,000

3 $20,000 $2,000

4 $25,000 $4,000

5 $30,000 $8,000

6 $35,000 $16,000

7 $40,000 $32,000

8 $45,000 $64,000

9 $50,000 $128,000

10 $55,000 $256,000

11 $60,000 $512,000

12 $65,000 $1,024,000

13 $70,000 $2,048,000

14 $75,000 $4,096,000

15 $80,000 $8,192,000

16 $85,000 $16,384,000

17 $90,000 $32,768,000

18 $95,000 $65,536,000

19 $100,000 $131,072,000

20 $105,000 $262,144,000

21 $110,000 $524,288,000

22 $115,000 $1,048,576,000

23 $120,000 $2,097,152,000

24 $125,000 $4,194,304,000

Answer 2

8th Month

Explanation:

We will calculate the payments by both the method as shown below

Company A

$10,000 + $ 5000 = $ 15000

$ 15000 + $5000 = $20,000

$20,000+ $5000 = $25,000

$25,000 + $5000 = $30,000

$30,000 + $5000 = $35,000

$35,000 + $5000 = $40,000

$40,000 + $5000 = $45,000

$45,000 + $5000 = $45,000 = $ 50,000

$ 50,000 + $ 5000 = $ 55,000

Company B

$ 500

2 x $ 500 = $1000

2 x $1000 = $2000

2 x $2000 = $4000

2 x $4000 = $8000

2 x $8000 = $ 16,000

2 x $ 16,000 = $ 32,000

2 x $ 32,000 = $ 64,000

2 x $ 64,000 = $128,000

Thus, it is the 8th month during which Company B's payment first exceed Company A's payment