Hi,
<Does $1004 make sense?>
That's what i am saying. I have shown you my work. Show me yours or tell me where i am wrong.

I have calculated again for Ammy:
P=1000, t=1( annual), n=2 (compounded 6 months), r=8%=0.08
A= 1000(1+0.08/2)^2= 1000(1.04)^2=1.0816= 1081.6 (wrong answer)
Okay now i realize that the other poster(wayneh) was right, n should be 1 not 2, becaue we are calculating interest for only 6 months not the whole year.
So it should be:
P=1000, t=1( annual), n=1 (compounded 6 months and we are calculating only for the 1st period not the whole year), r=8%=0.08
A= 1000(1+0.08/2)^2= 1000(1.04)^1=1040
This is correct.
For Bob:


P=1000, n=2(compounded quarterly , so 4 times but we have to calculate for 6 months so n=2, r=0.08, t=1

Now A = P (1 + r/n)^ (nt)

A= 1000(1 + 0.08/2)^(2*1)
This is giving a wrong answer. Some body please guide me

Zulfi.

 

You are saying that, after half a year, Bob only earned $4 on a deposit of $1000. That's 0.4% of interest after half a year when his interest rate is 8% per year. Does that make sense? It's a simple question. If I promised you an 8% return each year on money you invested with me and you gave me $1000, would you feel that I was holding up my end if, after half a year, I claimed I only owed you $4 in interest?

I have told you, step by step, what to do to get the value in Bob's account after the six month period of interest. You have opted not to even attempt to do the first step. So I am done.

 

Hi,
<I have told you, step by step, what to do to get the value in Bob's account after the six month period of interest. You have opted not to even attempt to do the first step. So I am done.
>
Thanks for your work. My friend you are moving me in a wrong direction. We dont have to do step by step. We have to use the formula. And i have a problem in the formula i cant understand about the value of 'n'. In my view 'n' should be 2 because it says quarterly (i.e after 3 months so 4 periods in a year) but we have to calculate for 6 months (so only 2 periods. Thats why i have taken n=2). But actually n should be 4 to get the correct answer. I cant understand this why n should 4?

Zulfi.

 

Compare your entries in the formula with the definitions in the formula that I already gave you....

Compound interest formula: A = P (1 + r/n)^ (nt)

Where:

A = the amount of money that Bob has after 6 months, because the problem asks how much he has after 6 months.
P = the original amount of money that Bob invested (principal) -??
r = the annual interest rate = ?? (that is a 12 month rate)
n = the number of times that interest is compounded per year - ??
t = the number of years the money is invested - ??
_____________________
You answered..

For Bob:
P=1000, n=2(compounded quarterly , so 4 times but we have to calculate for 6 months so n=2, r=0.08, t=1
Now A = P (1 + r/n)^ (nt)
A= 1000(1 + 0.08/2)^(2*1)
This is giving a wrong answer. Some body please guide me
_______________

A = the amount of money that Bob has after 6 months, because the problem asks how much he has after 6 months.
P = the original amount of money that Bob invested (principal) -You said 1000 - correct
r = the annual interest rate = ?? (that is a 12 month rate) - you said 0.08 - correct
n = the number of times that interest is compounded per year - you said 2 - INCORRECT
t = the number of years the money is invested - you said 1 - INCORRECT

Why have you made these errors? In the case of n, you said, "n=2(compounded quarterly , so 4 times but we have to calculate for 6 months so n=2"

n = the number of times that interest is compounded per year - the original question says "compounded quarterly" and you correctly understood that as 4 times per year, but you decided to add your own interpretation to the formula and make n=2. So even though you understood that n=4, you decided to change it to n=2. The correct value is n=4.

In the case of t, you said "t=1".

t= the number of years the money is invested - the original question asked how much money Bob will have after 6 months. You know that as you said "for six months we have to calculate for 6 months". You used t=1. So, even though you understand that 6 months does not equal 1 year, you decided to use t=1. The number of years the money is invested is 0.5 because 6 months=.5 years. The correct value is t=.5.

Compound interest formula: A = P (1 + r/n)^ (nt)

A= 1000 * ( (1 + (0.08/4) )^(4 *.5) )
= 1000 * (1.02^2)
= 1000 * 1.0404
= 1040.40

If you learn the definitions for the terms in the formula and you stick to those definitions, you will have a much easier time getting the correct answer..

If you disregard the definitions for the terms in the formula and you decide to change them based on overthinking, or reading something that is not there, or wanting to make it harder than it is, you will continue to get wrong answers.

If you stick to the definitions in the formula, you can easily answer extensions of the question such as, how much do Amy and Bob have after 3 years or 10 years.

Finally, please understand that the people responding in this thread already know how to answer the question, you do not. It is difficult to know what you are thinking or how it is easiest for you to get the concepts, so sometimes we question you about how you got the answers you got and those questions are not because we can't see what you wrote, they are because we don't know how you could have come up with what you wrote.

 

Hi,
<I have told you, step by step, what to do to get the value in Bob's account after the six month period of interest. You have opted not to even attempt to do the first step. So I am done.
>
Thanks for your work. My friend you are moving me in a wrong direction. We dont have to do step by step. We have to use the formula. And i have a problem in the formula i cant understand about the value of 'n'. In my view 'n' should be 2 because it says quarterly (i.e after 3 months so 4 periods in a year) but we have to calculate for 6 months (so only 2 periods. Thats why i have taken n=2). But actually n should be 4 to get the correct answer. I cant understand this why n should 4?

Zulfi.

Well, I don't want to move you in the wrong direction and risk having you actually understand what you are doing and the formula you are using. That would be a travesty. And heaven forbid you actually go through and get the right answer by some other means so that you have something to compare your answer using your formula to so that you can check your own work instead of having to ask others if your answer is correct. We absolutely can't have that.

If someone DID want to understand the formula, I would tell them what I've already tried to tell you. You need to first calculate the interest rate PER COMPOUNDING PERIOD, known as the PERIODIC INTEREST RATE. If the interest is compounded quarterly, there are FOUR compounding periods per year, so the rate PER COMPOUNDING PERIOD is the annual rate divided by four. This is the PERIODIC INTEREST RATE. This has NOTHING to do with how long the money is left there. To calculate the value after at the end of the of a certain amount of time, you use the PERIODIC INTEREST RATE in the formula and the exponent is the number of compounding periods that have elapsed, which is TWO in this case.

So you need to use both FOUR and TWO in order to get the right answer, but you need to use them correctly. Unfortunately, using them correctly is a lot easier when you understand the formula you are using, which is apparently not something you are interested in doing.

 

Geezz.. I got dizzy reading all your ideas.But I should say that this is more stimulating than listening to my teacher.

 

Okay now i realize that the other poster(wayneh) was right, n should be 1 not 2, becaue we are calculating interest for only 6 months not the whole year.
So it should be:
P=1000, t=1( annual), n=1 (compounded 6 months and we are calculating only for the 1st period not the whole year), r=8%=0.08
A= 1000(1+0.08/2)^2= 1000(1.04)^1=1040
This is correct.

Excellent! Except you left the 2 in the formula as highlighted. You now just need to apply the same process to Bob.

For Bob:
P=1000, n=2(compounded quarterly , so 4 times but we have to calculate for 6 months so n=2, r=0.08, t=1

Now A = P (1 + r/n)^ (nt)

A= 1000(1 + 0.08/2)^(2*1)
This is giving a wrong answer. Some body please guide me

The rate that gets raised to a power is one plus the annual rate divided by the number of compounding periods per year, not the rate divided by the number of elapsed periods. The exponent is then the total number of elapsed compounding periods. This makes the units work out: Inside the parentheses is the gain in one compounding period, the exponent is the number of compounding periods that has elapsed.

 

Hi,
Thanks for you people in taking interest in my problem. God bless you all. Despite providing the complete definition of all elements in the formula, maybe i did not read it properly as pointed out by WBahn. Thanks Mr. Wayneh for pointing out my mistakes, may be because i was not able interpret the things clearly as specified by Mr. Raymond. In view of this I have done it again:

For Amy:

A = the amount of money that Ammy has after 6 months, because the problem asks how much he has after 6 months.=?
P = the original amount of money that Amy invested (principal) -1000
r = the annual interest rate = ?? (that is a 12 month rate) =0.08
n = the number of times that interest is compounded per year = 2
t = the number of years the money is invested =.5A = P (1 + r/n)^ (nt)
A= 1000(1+0.08/2)^(2 *1/2)
A= 1000(1+0.04) ^1 = 1000 (1.04) = 1040

For Bob:
A = the amount of money that Bob has after 6 months, because the problem asks how much he has after 6 months.=?
P = the original amount of money that Amy invested (principal) -1000
r = the annual interest rate = ?? (that is a 12 month rate) =0.08
n = the number of times that interest is compounded per year = 4
t = the number of years the money is invested =.5
A = P (1 + r/n)^ (nt)
A= 1000(1+0.08/4)^(4*1/2) = 1000(1+0.02)^2 = 1000(1.02)^2 = 1.0404=1040.4
I think I am right this time.

Now difference =A=1040-1040.4=0.4

Zulfi.

 

1000(1+.08/2) ^( 2 * .5) = $1040 for Amy
1000(1+.08/4) ^(4*.5) = $1040.4 for Bob

6 months = .5 year
semi anually = 2 in a year
quarterly = 4 in a year

 

Hi,
Thanks for you people in taking interest in my problem. God bless you all. Despite providing the complete definition of all elements in the formula, maybe i did not read it properly as pointed out by WBahn. Thanks Mr. Wayneh for pointing out my mistakes, may be because i was not able interpret the things clearly as specified by Mr. Raymond. In view of this I have done it again:

For Amy:

A = the amount of money that Ammy has after 6 months, because the problem asks how much he has after 6 months.=?
P = the original amount of money that Amy invested (principal) -1000
r = the annual interest rate = ?? (that is a 12 month rate) =0.08
n = the number of times that interest is compounded per year = 2
t = the number of years the money is invested =.5A = P (1 + r/n)^ (nt)
A= 1000(1+0.08/2)^(2 *1/2)
A= 1000(1+0.04) ^1 = 1000 (1.04) = 1040

For Bob:
A = the amount of money that Bob has after 6 months, because the problem asks how much he has after 6 months.=?
P = the original amount of money that Amy invested (principal) -1000
r = the annual interest rate = ?? (that is a 12 month rate) =0.08
n = the number of times that interest is compounded per year = 4
t = the number of years the money is invested =.5
A = P (1 + r/n)^ (nt)
A= 1000(1+0.08/4)^(4*1/2) = 1000(1+0.02)^2 = 1000(1.02)^2 = 1.0404=1040.4
I think I am right this time.

Now difference =A=1040-1040.4=0.4

Zulfi.

Correct!

Except that the difference, as you have defined it on the last line, is negative (you subtracted a larger number from a smaller number). But read the problem again and look at what they asked for -- how much more money does Bob have than Amy. So what SHOULD you final equation be?

 

Just $0.4 in 6 months.