Applications of Exponential Equations You are offered a new

Applications of Exponential Equations You are offered a new job. The prospective boss says, \"I will pay you $1,000,000 for one month\'s work OR I will pay you $2.00 the first day, $4.00 the second day, $8.00 the third day, and each day double the pay I gave you the day before. Which would you prefer?\" Assuming there are four full 5-day work weeks in the month what do you tell this potential boss? You decide you want to do some work on your house. The contractor says that the job will cost about $2500. You can either go to the credit union and take out a home equity Joan at 3.5% that is compounded monthly but you will have to borrow at least $5000. Or you can charge the exact amount on your Visa card at 13.5% compounded daily. If you don\'t make any payments on the borrowed amount for one year what would be the interest accrued for each financing option? Which is the better deal?

Solution

1) 1day -- $ 2.00

2nd day ---$ 4.00 day

3rd day --- $ 8.00 day

geometric progression (r) = 4/2 = 8/4 = 2

first term ao = $ 2.00

no.of days =20

Sum of geometric progression = 2(1- 2^20)/(1-2) = $ 2097150

So, with this option i would get $ 2097150 and with one month time payment $ 1,000,000

So, option of $2.00 on 1st day , $ 4.00 on 2nd day,$ 8.00 day on 3rd day...is a better option