Question

Mike started a savings account by depositing $9. Each month he deposits more money than the month before. At the end of 41 months, he has saved $9,989.00. How much more does he deposit each month?

A.$11.00

B.$11.50

C.$12.00

D.$12.50

Answer 1

I am having trouble understanding this...if each month he deposits more money then the month before, then he is not depositing the same amount of money each month...right ?

Answer 2

Yes because its an Arithmetic Series

Answer 3

There is insufficient information in the problem statement to state that it is an arithmetic series. Is it really? It might say that, I suppose.

Answer 4

Well the topic for this lesson is "08.02 Arithmetic Series" and i just copied and pasted the question

Answer 5

Fair enough. It should be written more clearly. Any way...

How do you propose we proceed with this? Have you a formula for a sum of 41 payments in an arithmetic series or shall we build it?

Answer 6

Are your answer choices supposed to be the common differences ?

Answer 7

The formula is to find the sum is Sn=n/2( a1 + an)

Answer 8

and I'm guessing the answer choices is the amount of money he deposits each month

Answer 9

there it is the formula

Answer 10

No i am pretty sure you're right. I just don't know how we're suppose to figure out how much he put in each month

Answer 11

Lets up so

Answer 12

hope**

Answer 13

the only way I am getting 469 as the 41st term is if I use 11.50 as the common difference
But when I add the sums of the 41st terms, I am ending up with 9799 instead of 9989.

Answer 14

and when I use 12 as the common difference, I am ending up with over 10,000 as the sum of 41 terms.

Answer 15

I'll just guess its only one question But thank you guys so much for trying to solve it

Answer 16

I am sorry that I could not help :(

Answer 17

Let N be the common difference in the payments.

Add them up!

9
9+N
9+2N
9+3N
...
9+40N
9+41N

That's 42 deposits.

9(42) + N(1 + 2 + 3 + ... + 40 + 41) = 378 + N((41*42)/2) =
378 + N(41*21) = 378 + 861N

Finally:

378 + 861N = 9989 and N = 11.1626

I know, you're thinking, "Why did we go all the way to 42 payments?" Well, suppose we don't and we cut off at the slightly more motivated 41 payments...

369 + 820N = 9989 and N = 11.7317

Where does that leave us?

I show:

41 Payments

11.00 ==> 9389
11.50 ==> 9799
12.00 ==> 10209

42 Payments

11.00 ==> 9849
11.50 ==> 10279.50

So, $9989.00 ? I'm not seeing it.

Answer 18

I put 11.50$ as the answer and it was incorrect :/

Answer 19

Its no problem! thank you everyone

Answer 20

hmm....I got 11.50 as the closest answer, and when I used 12 as the common difference, it was over 10,000.

Answer 21

Except that makes no sense. We are adding whole dollars or half dollars. It is not acceptable for ANY deposit to end with 0.265. 11.50 is no good.

9 + 40*11.50 = 469

This is not a good question. Something seriously wrong with it.

Answer 22

I took the test and the correct answer is $11.00