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## #1 2019-09-10 12:51:48

Hannibal lecter
Member
Registered: 2016-02-11
Posts: 274

### bank interests

Hi,

A bank account starts out with \$10,000. Interest is compounded monthly at 6 percent per year (0.5 percent per month)

what is compounded monthly at 6 percent per year!
it's compounded  monthly! why he wrote next 6% per year!

what is the meaning of that

is that mean the 10,000 will be 10500 than after a year it will be \$10500  * 12months  = \$126000
after that I will add the 6% to the \$126000??? = \$133560

I don't think I'm right lol I'm just saying hehe
can u help it's very important I felt nervous because I didn't understand that
can you please analyse the question for me

Wisdom is a tree which grows in the heart and fruits on the tongue

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## #2 2019-09-10 13:00:06

Hannibal lecter
Member
Registered: 2016-02-11
Posts: 274

### Re: bank interests

and the full exercise is :

Write an algorithm to settle the following question: A bank account starts out with \$10,000. Interest is compounded monthly at 6 percent per year (0.5 percent per month). Every month, \$500 is withdrawn to meet college expenses. After how many years is the account depleted?

the problem is I don't want only the answer I want to analyse the answer and the steps to have fully understand about that problem

Wisdom is a tree which grows in the heart and fruits on the tongue

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## #3 2019-09-10 19:26:05

bob bundy
Registered: 2010-06-20
Posts: 8,636

### Re: bank interests

hi Hannibal lecter

So that savers can compare schemes it is usual to state the yearly (annual) rate of interest.  Some schemes then calculate and add interest once per year.  But some schemes add interest every month, so it is necessary to state what rate will be applied for this.  I live in the UK and here there is a formula that does this.  It's more complicated than what is given in your question so I won't confuse you by describing it now.  The USA system for working out a monthly rate is to divide the yearly rate by 12.  Thus 6% per year becomes 0.5% per month.

Each month this is what happens:

Add interest from the previous period.
Subtract \$500.
This gives the new amount that will apply for the next interest calculation, one month later.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #4 2019-09-11 14:41:38

Hannibal lecter
Member
Registered: 2016-02-11
Posts: 274

### Re: bank interests

oh I didn't notice that how could I didn't focus I was focus in read this but u helped me finally

I have another question
the account won't be depleted because when we add 500 to 10,000
than sub 500
nothing will change the account won't be \$0

what is the value in the question that I can change to make the account depleted ?

Wisdom is a tree which grows in the heart and fruits on the tongue

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## #5 2019-09-11 19:43:46

bob bundy
Registered: 2010-06-20
Posts: 8,636

### Re: bank interests

The interest after the first month is \$50 not \$500.

10000 x 0.5/100 = 50

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #6 2019-09-12 03:57:11

Hannibal lecter
Member
Registered: 2016-02-11
Posts: 274

### Re: bank interests

but please look at this this :-

Consider the question in Exercise R1.12. Suppose the numbers (\$10,000, 6 percent, \$500) were user selectable. Are there values for which the algorithm you developed would not terminate? If so, change the algorithm to make sure it always terminates

it was the next question after that
what the question want from me to do?

Wisdom is a tree which grows in the heart and fruits on the tongue

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## #7 2019-09-12 06:04:11

bob bundy
Registered: 2010-06-20
Posts: 8,636

### Re: bank interests

Let's try an algebraic approach.

Let the initial amount in the account be P; the monthly interest rate be r; and the amount taken out each month be M.

At the end of each month

new amount in the account = old amount plus interest less the monthly amount out

P_new = P_old + (P_old x r/100) - M

If P_new is to be the same as P_old then

P = P + P x r/100 - M

So M = P x r/100

If I choose P = 10000 and r = 0.5 then

M = 10000 x 0.5/100 = 100 x 0.5 = 50

So the algorithm will not end if M = 50

You could vary a different value.

If r = 0.5 and M = 500 then

500 = P x 0.5/100 = P/200  so P = 100,000

So if you have a much bigger amount saved then the interest earned can exactly cover the monthly amount out.

In the above I have kept the P constant from month to month.  You could also let the amount in the account grow.  So P = 10000, r = 0.5, M = 40 means that P will grow, month by month.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #8 2019-09-13 14:39:31

Hannibal lecter
Member
Registered: 2016-02-11
Posts: 274

### Re: bank interests

you said :

new amount in the account = old amount plus interest less the monthly amount out

you mean : p_new = 10000 + 10050 - 500 = 19550 ?

but I thought the  amount will be only : 10000 + 0.5% = 10050 in the first month

you are saying old amount plus interest
why did you put two p_old!

sorry but I didn't understand the first movements

it's like you rote p_new = p_old + M - M !
because M = ( p * r/100 )
why this step?

can you give me values step by step for the first 3 months please

before that pls see how is my calculations :-

balance = 10,000 + 0.5% = 10050
now 10050 - \$500 = 9950
now add 9950 + 0.5% = 9597.75
after that again sub 9597.75 - \$500
to the end....
and in my calculations the algorithm will stop because the account balance will be less than \$500 so can't withdraw from it again

what is wrong in my calculations?

Last edited by Hannibal lecter (2019-09-13 15:57:04)

Wisdom is a tree which grows in the heart and fruits on the tongue

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## #9 2019-09-16 02:27:26

bob bundy
Registered: 2010-06-20
Posts: 8,636

### Re: bank interests

hi

I used Microsoft Excel to do a few years' calculations.  I have made an image of these and alongside the formulas I used to do the calculations.

You should be able to see that the 'Principle' is gradually going down but not as fast as you thought.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #10 2019-09-16 13:06:22

Hannibal lecter
Member
Registered: 2016-02-11
Posts: 274

### Re: bank interests

thank you very much

Wisdom is a tree which grows in the heart and fruits on the tongue

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## #11 2019-09-23 12:47:14

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,633

### Re: bank interests

Hi Bob and Hannibal;

bob bundy wrote:

I used Microsoft Excel to do a few years' calculations.

That would be "a few months' calculations", Bob.

bob bundy wrote:

You should be able to see that the 'Principle' is gradually going down but not as fast as you thought.

I try not to drop my principles, but this \$10,000 principal fairly plummeted! Test spotted, Bob!

Hannibal lecter (post #8) wrote:

balance = 10,000 + 0.5% = 10050
now 10050 - \$500 = 9950
now add 9950 + 0.5% = 9597.75
after that again sub 9597.75 - \$500

The algorithm is right, but there are two errors in the figures. They should read:

balance = \$10,000 + 0.5% = \$10050
now \$10050 - \$500 = \$9550
now add \$9550 + 0.5% = \$9597.75
after that again sub \$9597.75 - \$500

Hannibal lecter (post #2) wrote:

Every month, \$500 is withdrawn to meet college expenses.

The problem doesn't say at which end of the month the money is withdrawn, but the timing makes a difference to the amount of interest earned, as shown in my image below by comparing the column D and E figures.

This interest difference can affect the month in which a zero balance is reached: eg, for withdrawals of \$501 instead of \$500, the column D algorithm reaches a zero balance in the month prior to column E's zero balance.

Btw, Excel has a handy function that calculates the number of periods (months, in this case) for the bank balance to reach zero. It gives the same answers as Hannibal's and Bob's algorithm (the same as my algorithm B) and also my algorithm A...which is comforting to know.

Enter the function into one cell for algorithm A and another cell for algorithm B. The respective solution for each algorithm will be displayed in whole + part months.

Last edited by phrontister (2019-10-01 16:09:13)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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## #12 2019-09-23 21:58:13

bob bundy
Registered: 2010-06-20
Posts: 8,636

### Re: bank interests

hi Phro,

Thanks for the analysis.  I had thought the calcs would be different if the sum is subtracted at the start of each month but was worried it might confuse HL.  As this is the fault of the question setter it shouldn't cost any credit.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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