A student's parents offer him one of two options to receive scholarship money for college.
Option A: Deposit $10,000.00 into his savings account and then add an additional $750.00 each day for 30 days
Option B: Deposit $1.00 into his savings account and then double that amount each day for only 15 days
When rounded to the nearest cent, how much money is deposited into his savings account on the last day (day 30) for Option A, and how much is deposited into his savings account on the last day (day 15) for Option B? If the student keeps only what is deposited on the last day, which option should he choose?
Option A Versus Option B
Option AOption B
DayAmount DepositedDayAmount Deposited
A = $32,500.00, B = $32,768.00; B, because he receives $268.00 more A = $22,500.00, B = $30.00; A, because he receives $22,470.00 more A = $32,500.00, B = $42,768.00; B, because he receives $10,268.00 more A = $87,549.55, B = $32,768.00; A, because he receives $54,781.55 more
I think your teacher made a mistake in Option 2. I believe he/she computed 2^15 =$32,768 as the amount of money in the account on the 15th day. But that is NOT so, if you begin with a deposit of $1 on day 1 and on the 15th day, you will have:2^(15-1) =$16,384. You can easily list them and see for yourself: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1,024, 2,048, 4096, 8,192, 16,384(15th day deposit). I think what they did was simply raise 2^15 =$32,768. This would have been true if the first day's deposit was $2 instead of $1.
Optio A is a straightforward as: $750 x 30 + $10,000 =$32,500(on 30th day)
Because a mistake appears to have been made, then Option A is obviously the better deal.
Well....if the student is to keep only the amount deposited the last day, Option B is by far better
But.....I think the problem's intent is to show the total amount in both accounts after the last deposit and to compare those...
Guest is correct as to the amount on deposit at the end for option A = $ 32500
But for Option B....the total amount on deposit at the end for Option B is :
$ [2^15 - 1 ] = $32767
Thus.....Option B is better by $267