compounded quarterly interest in summation notation

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btrfly24

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I've done the whole problem down to needing to write this in summation notation.

6270.15 compounded quarterly for 3 years at 4%. It sounds so easy and I can figure out the answer, just not how to write the equation in summation notation. This is a geometric series right? And I can write the equation for the sum, but that's as far as I can get, maybe because it's so early in the morning?? Please point me in the right direction! Thanks so much. Catherine.
 
btrfly24 said:
I've done the whole problem down to needing to write this in summation notation.

6270.15 compounded quarterly for 3 years at 4%. It sounds so easy and I can figure out the answer, just not how to write the equation in summation notation. This is a geometric series right? And I can write the equation for the sum, but that's as far as I can get, maybe because it's so early in the morning?? Please point me in the right direction! Thanks so much. Catherine.
Click to expand...
Summation notation? I don't think so. Are you making multiple deposits or withdrawals? It appears to me that you have only one cash flow.

\(\displaystyle 6270.15*(1+\frac{0.04}{4})^{(3*4)}\)

Where were you planning to put a summation? Perhaps you have not provided the entire problem statement?
 
Hello, btrfly24!

Write in summation notation: $6270.15 compounded quarterly for 3 years at 4%.
Click to expand...

The periodic interest rate is: \(\displaystyle \;i \,=\,\frac{0.04}{4} \,=\,0.01\)
The number of periods is: \(\displaystyle \,3\,\times\,4\:=\:12\)

Let \(\displaystyle P\,=\,6270.15\)

The final amount is: \(\displaystyle \:A\:=\:p(1.01)\,+\,P(1.01)^2\,+\,P(1.01)^3 \,+\,\cdots\,+\,P(1.01)^{12}\)

In summation notation: \(\displaystyle \:p\L\sum^{12}_{n=1}\)\(\displaystyle (1.01)^n\)

 
But, but...that adds up the 12 "account balances" after the credit of interest: WHY ? :shock:

~6332.85 + ~6396.18 + .... + ~7065.36 = ~80316.41
Isn't 7065.36 what you're interested in ?
 
I did my arithmatic wrong...Let me just give the whole question:

Duane deposited $100 into an account paying 4% compounded quarterly each jan 1 for 8 consecutive years. Given that the first deposit was made jan 1 1990 and the last was jan 1 1997, write a series in summation notation whose sum is the amount in the account on Jan 1 2000.

I get this far:

100+100(1.01)+100(1.01)^2+...100(1.01)^32

100(1-(1.01)^32) all over (1-1.01) = 3749.41 right?

Then do I just do the same thing for the 3749.41 but only for 12 quarters?
 
You seem a little confused. You must get your payments and accumulations to match up correctly.

1) The payments are annual.
2) The compounding is quarterly

If you do nothing to adjust for this mismatch, you will not get the right answer.

1.01 is a quarterly accumulation factor.
1.01^4 is an annual acumulation factor. This is the one you need.

Ponder a payment at a time, if necessary.

1/1/1990 100*(1.01^4)^10 Value at 1/1/2000
1/1/1991 100*(1.01^4)^9 Value at 1/1/2000
1/1/1992 100*(1.01^4)^8 Value at 1/1/2000
...
1/1/1997 100*(1.01^4)^3 Value at 1/1/2000

Note: It irritates me a little in an accumulation problem that the payments often are written backwards with respect to time. It's not wrong, but I think it makes a little less sense. My suggestion would be to write what you have, 100+100(1.01)+...+100(1.01)^32 in the opposite direction, 100(1.01)^32+100(1.01)^31+...+100(1.01)+100. Just a thought. I am aware of no official standard.
 
you're right when you said I was confused!! It totally makes sense to write it backwards! This REALLY makes sense now!! Thanks so much!
 
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