1. math problem

in the start of the year you put 20000 in your bankaccount that has a intrest of 4%. You lift every year 2500euros How much do you have left after 8 lifts?

2. Originally Posted by Rambo
in the start of the year you put 20000 in your bankaccount that has a intrest of 4%. You lift every year 2500euros How much do you have left after 8 lifts?
Let's do this in 2 parts. Since you requested a series, and not the annuity formulas, I'll do it that way for you.

First, take the accumulated value of 20,000 each year at 4% for 8 years.

Do your series with 20000*1.04^1 + 2500*1.04^2 + ......

You should get 9.582795311

Multiply the series by your 20000 payment, and you have accumulated 191655.9062 at time 8.

That's part 1. For part 2, do the same, but with your 2500 payment instead.
Try that and let me know.

3. no i do not get 9.????

can you write the whole thing again please

4. Originally Posted by mathceleb
Let's do this in 2 parts. Since you requested a series, and not the annuity formulas, I'll do it that way for you.

First, take the accumulated value of 20,000 each year at 4% for 8 years.

Do your series with 20000*1.04^1 + 2500*1.04^2 + ......

You should get 9.582795311

Multiply the series by your 20000 payment, and you have accumulated 191655.9062 at time 8.

That's part 1. For part 2, do the same, but with your 2500 payment instead.
Try that and let me know.
with lift i mean withdraw

5. is this correct?

200000*1.04^8=27371.38

27371.38/(1/(1.04)^1+1/(1.04)^2+1/(1.04)^3+1/(1.04)^4+1/(1.04)^5+1/(1.04)^6+1/(1.04)^7+1/(1.04)^8))=28472.00641

27371.38-28472.00641=1100.626

IS THIS CORRECT????

6. Originally Posted by Rambo
200000*1.04^8=27371.38

27371.38/(1/(1.04)^1+1/(1.04)^2+1/(1.04)^3+1/(1.04)^4+1/(1.04)^5+1/(1.04)^6+1/(1.04)^7+1/(1.04)^8))=28472.00641

27371.38-28472.00641=1100.626

IS THIS CORRECT????
I misunderstood your original question text.

Because you take out payments at the end of the year, and you invested the 20000 at the beginning of the year, your investment is 20000*1.04^9

The beginning of the 9th year is the end of the 8th year.

7. Originally Posted by mathceleb
I misunderstood your original question text.

Because you take out payments at the end of the year, and you invested the 20000 at the beginning of the year, your investment is 20000*1.04^9

The beginning of the 9th year is the end of the 8th year.
you withdraw the money 8 times not 9 times!!!????

Is my math correct?

8. Originally Posted by Rambo
you withdraw the money 8 times not 9 times!!!????

Is my math correct?
Rambo,

Your initial deposit is at time 0. Beginning of Year. Your first deposit is at the end of year 1. Therefore, your initial deposit has already had 1 year of interest. So, when your last withdrawal at the end of year 8 occurs, your initial deposit at time 0 has already had 9 years to accumulate interest.

Also, you are accumulating in this problem, not discounting. Therefore, your series;

(1/(1.04)^1+1/(1.04)^2+1/(1.04)^3+1/(1.04)^4+1/(1.04)^5+1/(1.04)^6+1/(1.04)^7+1/(1.04)^8))= should not have 1/'s in it.

it should be:

(1.04)^1+(1.04)^2+(1.04)^3+(1.04)^4+(1.04)^5+(1.04 )^6+(1.04)^7

Since your withdrawals are at the end of the month, your time is 1 less.

9. I put the money to the account in THE BEGINNING of the year and 8 years forward i withdraw 2500euros.
And if you take 2500euro every year 8 years forward form the account it is discounting!!!!

10. Originally Posted by Rambo
I put the money to the account in THE BEGINNING of the year and 8 years forward i withdraw 2500euros.
And if you take 2500euro every year 8 years forward form the account it is discounting!!!!
No, you are projecting both balances to end of year 8 with interest.

11. Originally Posted by mathceleb
No, you are projecting both balances to end of year 8 with interest.
Yes and then counting them - eachother.

12. please solve the whole thing using series so i see what you mean write out every calculation please.

13. Originally Posted by mathceleb
Rambo,

Your initial deposit is at time 0. Beginning of Year. Your first deposit is at the end of year 1. Therefore, your initial deposit has already had 1 year of interest. So, when your last withdrawal at the end of year 8 occurs, your initial deposit at time 0 has already had 9 years to accumulate interest.

Also, you are accumulating in this problem, not discounting. Therefore, your series;

(1/(1.04)^1+1/(1.04)^2+1/(1.04)^3+1/(1.04)^4+1/(1.04)^5+1/(1.04)^6+1/(1.04)^7+1/(1.04)^8))= should not have 1/'s in it.

it should be:

(1.04)^1+(1.04)^2+(1.04)^3+(1.04)^4+(1.04)^5+(1.04 )^6+(1.04)^7

Since your withdrawals are at the end of the month, your time is 1 less.

how do you assume the withdrawals are at the end of month?

14. Originally Posted by mathceleb
No, you are projecting both balances to end of year 8 with interest.
My opinion is that the withdrawals are 8 when it says so in the text!

15. so the answer is 20000*1.04^9=28466.236

28466.236(1.04)^1+...+(1.04)^8=32028.10557