Future value annuities

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panda125

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ABC company plans to make four annual deposits of 2000 dollars each to a special building fund. The fund assets will be invested in mortgage instruments expected to pay interest at 12% on the fund balance. Determine how much will be accumulated in the fund on December 31,2014 under this situation:

The first deposit is made on December 31,2010, interest is compounded quarterly.

From what i understand so far this problem is a annuity due, because the payment is due right away. Because it being compounded quarterly this interest rate is at 3% with 16 periods, but every time i use a annuity table or formula i am getting the incorrect answer. The answer is suppose to be 10,846, hoping someone here can help me out please.
 
panda125 said:
From what i understand so far this problem is a annuity due, because the payment is due right away. Because it being compounded quarterly this interest rate is at 3% with 16 periods, but every time i use a annuity table or formula i am getting the incorrect answer. The answer is suppose to be 10,846, hoping someone here can help me out please.
Click to expand...
10,846 is correct; actually 10,845.49

You cannot use "3% with 16 periods"; you must find the equivalent rate with 4 periods (coincide with payments).
This way: 1.03^4 - 1 = 1.1255088... - 1 = .1255088... which is ~12.55% effective annually.
 
thank for you help, but im still a little confuse, would i take the effective rate of 12.55 % with 4 periods and use the formula to solve it?
 
You are required to think it through. See, Dennis, this is why I hate those formulas. Students just get too hung up on them too often.

i = 0.12

Compounded quarterly

i/4 = 0.03

Here, you have a choice, convert the interest to an annual equivalent, or just go with it the way it is.

Convert:

r = 1.03^4 = 1.12550881

Now construct: $2,000 * (r + r^2 + r^3 + r^4) = $2,000 ((r - r^5)/(1-r)) = $10,845.49243

Don't Convert. Write directly.

w = 1.03

$2,000(w^4 + w^8 + w^12 + w^16) = $2,000((w^4 - w^20)/(1-w^4)) = $10 845.49243

In any case, you must keep the interest crediting consistent with the payments.
 
Thanks for another way of solving it, but i was messing around with the number:
(1.03)^4= 1.1255-1- =.1255

2000((1+.1255)^4-1/(.1255))=9635.96

9635.96(1+.1255)=10845.30

I just don't which way would be more efficient, or if im just getting lucky
 
The most efficient way would be the way tha tyou understand and that you can do quickly and accurately under exam pressure.

You did what you were told by both tutors. What you ahve done is exactly what it going on under my "Convert" scenario, which is exacly what Dennis supported.

Most fundamentally, you need to understand it, not memorize it.
 
tkhunny said:
You are required to think it through. See, Dennis, this is why I hate those formulas. Students just get too hung up on them too often.
Click to expand...
Agree, TK, BUT seems that this is what happen in real-life...or should I say real-classroom!
Teacher starts by introducing "da formula" and has students get familiar with it...
later, the teacher shows HOW that formula was devised...some don't even bother!!
 
I cannot argue with that, Dennis. I think it a disservice to the student who actually cares. There are a few.
 
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