Answer:
$50 a year is the better option only until both equations intersect. After intersection happens the first option of $100 will be greater.
*GO WITH THE FIRST OPTION*($100 a year)
Explanation:
I think your question is what is the better option
Lets do some awesome Math:
lets represent the info in choice 1 in the equation y=mx+b
y= total cost at the end of eternity
m=slope or $100 in our case
x=# of years(eternity)
b= starting balance of $100
lets substitute our values:
y=100x+100
lets take "x" as 10
y=100(10)+100
y=1100
for 10 yrs u get paid 1,100
lets represent the info in choice 2 in the equation y=mx+b
y= total cost at the end of eternity
m=slope or $50 in our case
x=# of years(eternity)
b= starting balance of $200
lets substitute our values:
y=50x+200
lets take "x" as 10
y=50(10)+200
y=700
for 10 yrs u get paid 700
even though choice 1 seems like the better option lets find out where these points intersect using substitution: (intersection: for a shared value of "x" the y value will be same for both equations)
100x+100=50x+200
50x=100
x=2
if x=2 then y=300
P.O.I= (2,300)
lets take a value of x that is less than the value of intersection (2)
choice 1:
y=100(1)+100
y=200
choice 2:
y=50(1)+200
y=250
since the 2nd option is greater than the first we can concur that $50 a year is the better option only until both equations intersect. After intersection happens the first option of $100 will be greater.
