You have a rich aunt who wants to give you money. She o↵ers you two choices: Choice 1: You receive $100 starting today once a year every year for the rest of eternity. Choice 2: You receive $200 today and then $50 once a year starting next year for all of eternity

$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.

answer; yield to maturity;