Question

Lena has been offered a job with two salary options. Option 1 starts at $31,000 and has a $500 raise each year. Option 2 starts at $29,000 and has a 4% raise each year. Which pays more after 5 years?
Answer

Option 1, at $33,550

Option 2, at $33,550

Option 1, at $35,282

Option 2, at $35,282

Answer 1

Option 1, her salary increases 500 each year. So its arithmetic sequence with a = 31000, d = 500

can you find 5th term ?

Answer 2

the 5th term is 33000

Answer 3

one small catch here, since you want to know salary after 5 years, you will have to find 6th term. NOT 5th term

Answer 4

so 33500

Answer 5

Correct.

Option 1 : 33,500 -------------------------------(1)

Answer 6

lets find 6th term for Option2 also

Answer 7

but thats not a choice

Answer 8

29020

Answer 9

Option 2 starts at $29,000 and has a 4% raise each year.

a = 29,000
r = 1.04

\(a_n = a r^{n-1}\)
\(a_6 = 29000 (1.04)^{6-1}\)
= ?

Answer 10

29005

Answer 11

check again

Answer 12

http://www.wolframalpha.com/input/?i=29000%281.04%29%5E5

Answer 13

35282?

Answer 14

Yes

Answer 15

Option 2, at $35,282

Answer 16

thanks for the help

Answer 17

yw