SOLUTION: Hello Question Lisa was offered two payment options for a three month long job. If she chooses Option A, she will be paid 35,000 monthly. If she chooses Option B, she will be pa

Question 1183349: Hello
Question
Lisa was offered two payment options for a three month long job.
If she chooses Option A, she will be paid 35,000 monthly. If she chooses Option B, she will be paid 30,000 in the first month with an increase of 20% after each month
Which option pays more
Option A: 3 MONTHS
35,000 * 3=105,000
OPTION B: 3 MONTHS
30,000
30,000 * 1.2 = 36,000
36,000 * 1.2 = 43,200
$30,000+36,000+43,200=109,200
How I calculate option b is
30,000 M+
30,000 * 1.2=36,000 M+
36,000 * 1.2=43,200 M+
MR
When I do 1.2^2=1.44, it only gives me the final and 3rd month and not the grand total
Is there a better way to calculate the grand total?
Thanks in advance.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
for only 3 months, doing it the way you did it is fine.
the second option is also a geometric progression type formula.
in that formula:
An = A1 * r ^ (n-1)
in your problem:
A1 = 30,000
r = 1.2
n = 3
you get:
A3 = 30,000 * 1.2 ^ 2 =
there is also the sum formula that says:
Sn = A1 * (1 - r^n) / (1 - r)
in your problem:
n = 3
r = 1.2
A1 = 30,000
you get:
S3 = 30,000 * (1 - 1.2^3) / (1 - 1.2)
solve for S3 to get:
S3 = 109,200.

the formula is called a geometric sequence formula.
here's a reference.

https://www.mathplanet.com/education/algebra-2/sequences-and-series/geometric-sequences-and-series

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