+0  
 
0
1100
4
avatar
The problems is as follows:
A savings account has an interest rate of 5% compounded every six months. What amount should you deposit today so that you could withdraw $250 at the end of 6 months for the next 10 years.
I have the answer but I think the path I took to get the answer was to complicated.
I started with the basic compound interest formula:
S=P(1+r) n
Where:
S=value after n periods
P=the principal
r=the interest rate
n=the amount of periods
I since I am going to withdraw $250 at the end of each period and I want to gain another $250 on interest at the end of the next period I assumed that my value after n periods(S) to be:
S=P+250
Which converts my formula into
P+250=P(1+r) n
Then I tried to do some algebra to isolate P:
250 = P(1+r) n-P = P[(1+r) n-1]
250/P=(1+r) n-1
1/P=[(1+r) n-1]/250
P=[[(1+r) n-1]/250] -1
Plug in the values:
n=1
r=.025
(((1+.025)^1-1)/250)^-1
You can see I am totally ignoring the fact that the question says "for the next 10 years" I don't know if it is of any relevance to the answer or just there to distract. I think there is a simpler approach to this can anyone shed a light =)
 Jan 3, 2014
 #1
avatar+118654 
0
Hi randomstatistics,

This is an interesting question, and I like that fact that you have already had a good play with it.
I assume that $10000 is your answer is that right?
Have you looked at this logically to see if it could be right?
You are only going to get $250 twice a year for 10 years.
If you got no interest at all, how much money would you need in your account?
How much money do you want in the account at the end of 10 years. I am assuming that you didn't want any. Is that what you meant?
You have answered a good question, I am just not sure that it is the question that you intended. Do you know what question you have answered?
 Jan 3, 2014
 #2
avatar
0
Quote:

I assume that $10000 is your answer is that right?

Yep, 10,000 is the answer.

Quote:

Have you looked at this logically to see if it could be right?

If I understand the problem correctly the answer is indeed 10000. That amount of principal will generate 250 in interest every 6 months leaving the principal untouched always.

Quote:

If you got no interest at all, how much money would you need in your account?

To withdraw 500 a year, 250 every six months, for 10 years I would need 5000 but that would leave my account clean I think the problem wants me to leave the principal untouched and to withdraw only the interest

Quote:

How much money do you want in the account at the end of 10 years. I am assuming that you didn't want any. Is that what you meant?

I think the problem wants to leave the principal untouched, that is, the same amount at the beginning the same amount at the end.

Quote:

You have answered a good question, I am just not sure that it is the question that you intended. Do you know what question you have answered?

Good question =)
 Jan 3, 2014
 #3
avatar+118654 
0
okay I misunderstood, I thought you wanted to use up the interest as well as the principal in the 10 years.

You are also correct in thinking that you have turned a mole hill into a mountain.

I assume your logic is correct since you got the right answer but how about thinking of it like this.

You want to get $250 interest every 6 months because you will take that out and your principal will remain untouched.

I = P r t (You can use simple interest since you are only talking about 1 time period)
r = 0.025
t=1 (time period)
I = $250
P is unknown

250 = P * 0.025 * 1
P = 250 / 0.025
P= $10000

This is a little more straight forward I think.
 Jan 3, 2014
 #4
avatar
0
Melody:

okay I misunderstood, I thought you wanted to use up the interest as well as the principal in the 10 years.

You are also correct in thinking that you have turned a mole hill into a mountain.

I assume your logic is correct since you got the right answer but how about thinking of it like this.

You want to get $250 interest every 6 months because you will take that out and your principal will remain untouched.

I = P r t (You can use simple interest since you are only talking about 1 time period)
r = 0.025
t=1 (time period)
I = $250
P is unknown

250 = P * 0.025 * 1
P = 250 / 0.025
P= $10000

This is a little more straight forward I think.



Quote:

If you only have a hammer, you tend to see every problem as a nail.


Currently studying about compound interest, present' values, annuities, effective rates, made my mind a little bit inclined towards those formulas . Many thanks you made it look so simple! I guess the 10 year part of the problem was just there to distract, or I interpreted it wrong, but I doubt that! Thanks again!
 Jan 3, 2014

6 Online Users

avatar
avatar