Which is larger with initial investment

C

Carrie

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Here's the problem:
Which of the following investments is larger after 10 years?
A) An initial amount of $7200 is deposited with $3600 deposited annually, with interest earned at 3.5% compoounded annually.

B) An initial mamount of $$6,000 is deposited with $300 deposited monthly, with interest earned at #.5& compounded monthly.
The answer is A.

I caculated the interest earned without the initial investment and determined that A is larger after 10 years. I don't know and can't find how to account for the initial investment in cases A and B.

Thanks for any help.
Carrie
 
Please proofread your posts before submitting them.

(Use the Preview button.)

With all of the typographical errors in your post above, I am not willing to guess at what the actual numbers in this exercise are supposed to be (whether they make sense as you typed them above or not).
 
Please accept my apology. I am experiencing a miserable eye condtion. Things I normally find simple are more challenging. I did not, however, intend to make others suffer as well. Again, any help is truly appreciated.
Here's the problem:
Which of the following investments is larger after 10 years?
A) An initial amount of $7,200 is deposited with $3,600 deposited annually, with interest earned at 3.5% compoounded annually.

B) An initial amount of $6,000 is deposited with $300 deposited monthly, with interest earned at 3.5% compounded monthly.
The answer is A.

I calculated the interest earned without the initial investment and determined that A is larger after 10 years. I don't know and can't find how to account for the initial investment in cases A and B. I know how to use the annuity formula. However, the formula I have only accounts for equal periodic payments. I don't know how to account for the initial investment. I could do it for each period and then add as in a geometric sequence. However, if a problem like this were to be featured on a test, I wouldn't have time for that approach.

Thanks for any help.
Carrie
 
There is no need to "calculate the interest" as such; simply finding the FV (Future Value) is sufficient.
With your problem, we need to calculate FV's after 10 years.

> A) An initial amount of $7,200 is deposited with $3,600 deposited annually,
> with interest earned at 3.5% compounded annually.
Calculate the FV of 7200; formula: A(1+i)^n
7200 * 1.035^10 = 10,156.31
Calculate the FV of 10 annual deposits of 3600; formula: P((1+i)^n - 1) / i
3600 * (1.035^10 - 1) / .035 = 42,233.02

Add them up and that's the FV of case A)

> B) An initial amount of $6,000 is deposited with $300 deposited monthly,
> with interest earned at 3.5% compounded monthly.
The interest rate should be 3.5% ANNUAL, compounded monthly: that's important!

Proceed similarly to what I've done for case A).
Remember that the "n" will be 120 (120 months) and the "i" will be .035/12

In case you're not familiar with the "lettering":
A = present Amount
P = Payment (or deposit)
n = number of periods
i = interest rate per period
 
Thank you. I did not know if handling the amounts separately would adequately calculate the compounding. I truly appreciate your time.
Carrie
 
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