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March 11th, 2019, 09:56 PM   #1
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Finance theory

Hello

Can you help me please about the exercise:

A customer deposits 10,000 dollars each month for a year (Total is 12 deposits), when interest is 2%.
After the last deposit, the customer will start to withdraw the money each month for a year (12 withdrawals), when interest is 1%.
Two months after the last withdrawal, the customer will withdraw one time in the amount of 50,000 dollars, when interest is 1%.

What is the monthly withdrawal amount?
a. \$9,562
b. \$9,168
c. \$3,999
d. \$9,467
e. \$13,426

My solution:
12 deposits:


For getting \$50,000, the amount of money we need is:


134,120 - 50,500 = \$83,620

Therefore, the monthly withdrawal amount is (12 withdrawals):


Why I got wrong answer? I'm trying to understand for hours, and tried to solve in different ways, and I didn't get even one single correct answer.
I just used the basic formulas for calculating amounts of money with interests, there is nothing special, but if you didn't understand what I did, then tell me please and I will explain.
And if you didn't understand something because of some words (yeah, I'm not from country where I speak English every day, I'm sorry ), then tell me please and I will explain.

Thanks!

Last edited by skipjack; March 12th, 2019 at 03:14 AM.
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March 12th, 2019, 03:13 AM   #2
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If the 12 monthly deposits occur on the first day of 12 successive months, they don't cover a year until the 12th month ends. If the 12 monthly withdrawals start one month after the 12th monthly deposit, i.e. one year after the first monthly deposit, the 12th withdrawal occurs 11 months after the first withdrawal.
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March 12th, 2019, 11:22 AM   #3
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Problem statement is quite unclear.
From your 1st calculation : 10000 * [(1.02^12 - 1) / .02] = 134120
then the interest is 2% PER MONTH, and the 1st deposit is not immediate.
So the withdrawals during 2nd year will be similar: 1% per month, not immediate.

The transactions statement will look like this:
Code:
MONTH  TRANSACTION   INTEREST   BALANCE
  0                                    .00
  1           10000.00               .00     10000.00
  2           10000.00          200.00     20200.00
  3           10000.00          404.00     30604.00
....
 11          10000.00        2189.94    121687.15
 12          10000.00        2433.75    134120.90 : per your calc.
(rate changes to 1% per month)
 13          -8051.72        1341.21    127410.39
 14          -8051.72        1274.10    120632.77
....
 23          -8051.72          639.14     56501.51
 24          -8051.72          565.02     49014.81
(account to be terminated in 2 months)
 25                  .00          490.14     49504.95
 26                  .00          495.05     50000.00
 26        -50000.00               .00              .00
I can't follow your other calculations: they appear to be wrong.
As example, 49,014.81 is required at end of 2nd year
in order to end with 50,000.00 2 months later:
50000 / 1.01^2 = 49014.81

Then you need to calculate the required payment
that reduces 134120.90 to the above 49014.81,
which is 8051.72.

From the 5 choices provided. none is close to 8051.72
So there's something mysterious going on!

YOU need to find out from whoever gave you that problem to clarify:
is the interest rate compounded monthly?
are the deposits and withdrawals immediate
or delayed 1 month as we've both assumed?
Denis is offline  
March 12th, 2019, 01:33 PM   #4
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Quote:
Originally Posted by skipjack View Post
If the 12 monthly deposits occur on the first day of 12 successive months, they don't cover a year until the 12th month ends. If the 12 monthly withdrawals start one month after the 12th monthly deposit, i.e. one year after the first monthly deposit, the 12th withdrawal occurs 11 months after the first withdrawal.
Quote:
Originally Posted by Denis View Post
Problem statement is quite unclear.
From your 1st calculation : 10000 * [(1.02^12 - 1) / .02] = 134120
then the interest is 2% PER MONTH, and the 1st deposit is not immediate.
So the withdrawals during 2nd year will be similar: 1% per month, not immediate.

The transactions statement will look like this:
Code:
MONTH  TRANSACTION   INTEREST   BALANCE
  0                                    .00
  1           10000.00               .00     10000.00
  2           10000.00          200.00     20200.00
  3           10000.00          404.00     30604.00
....
 11          10000.00        2189.94    121687.15
 12          10000.00        2433.75    134120.90 : per your calc.
(rate changes to 1% per month)
 13          -8051.72        1341.21    127410.39
 14          -8051.72        1274.10    120632.77
....
 23          -8051.72          639.14     56501.51
 24          -8051.72          565.02     49014.81
(account to be terminated in 2 months)
 25                  .00          490.14     49504.95
 26                  .00          495.05     50000.00
 26        -50000.00               .00              .00
I can't follow your other calculations: they appear to be wrong.
As example, 49,014.81 is required at end of 2nd year
in order to end with 50,000.00 2 months later:
50000 / 1.01^2 = 49014.81

Then you need to calculate the required payment
that reduces 134120.90 to the above 49014.81,
which is 8051.72.

From the 5 choices provided. none is close to 8051.72
So there's something mysterious going on!

YOU need to find out from whoever gave you that problem to clarify:
is the interest rate compounded monthly?
are the deposits and withdrawals immediate
or delayed 1 month as we've both assumed?
Hm, I will write a complete question, maybe it will help (I wrote only the important things but it seems that I should write a complete question, I'm sorry about that, I didn't know that it was really necessary):

The Bank offers its customers a savings plan in which an amount of 10,000 dollars will be deposited every month for a year (total 12 deposits), but starting one year from now (in next year).
Only one year after the last deposit, the customer will start withdrawing the money. The withdrawals will be made every month
For a year (a total of 12 withdrawals), also, the customer will withdraw two months after the last withdrawal a one-time amount of 50,000 dollars (withdraw 50,000 dollars once).
What is the amount of monthly withdrawal, if the plan bears interest of 2% per month in the first two years (starting from today) and interest of 1% per month thereafter.

If you didn't understand something, tell me please.

Edit: Yes, I already checked it, this is a real question, I'm sorry for that I didn't write a complete question (I missed another important things), they tricked me with some words in question. I will try to solve it.

Last edited by IlanSherer; March 12th, 2019 at 01:44 PM.
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March 12th, 2019, 02:43 PM   #5
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Quote:
Originally Posted by IlanSherer View Post
The Bank offers its customers a savings plan in which an amount of 10,000
dollars will be deposited every month for a year (total 12 deposits), but
starting one year from now (in next year).
WHAT?!
So a customer waits 1 year, then starts this?!
You're either kidding or drunk

I suggest you get a girlfriend who is fluent in English,
and post your problem in proper English.

As is, makes no sense to me...
Denis is offline  
March 12th, 2019, 05:05 PM   #6
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Joined: Mar 2017
From: Israel

Posts: 85
Thanks: 2

Quote:
Originally Posted by Denis View Post
WHAT?!
So a customer waits 1 year, then starts this?!
You're either kidding or drunk

I suggest you get a girlfriend who is fluent in English,
and post your problem in proper English.

As is, makes no sense to me...
Lol I'm very sorry, it is: a customer doesn't want 1 year, he will start it after the last deposit.
They wrote in high level of our language and even I'm myself didn't understand it 100%, first time it happens to me.
IlanSherer is offline  
March 12th, 2019, 06:54 PM   #7
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Year#1 (Jan to Dec) : deposits $10,000 at end of each month ; earns 2% monthly

Year#2 (Jan to Dec) : withdraws $w at end of each month ; earns 1% monthly

Year#3 : earns 1% monthly; withdraws $50,000 at end of Feb, which closes account

Calculate w

If you're able to clearly post the problem in a way similar to above,
then come back....

IF the problem is exactly like above, then I've already given you the solution...
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