Suppose you buy a CD for $1000 that earns 2.5% APR and is compounded quarterly. The CD matures in 5 years. Assume that if funds are withdrawn before the CD matures, the early withdrawal fee is 3 months' interest. What is the early withdrawal fee on this account?

A. $3.75
B. $6.25
C. $3.13
D. $1.25

anywaysss lol @countonme123

i tried doing it my way i did it like this

1000+2.5*5-3

Question

Suppose you buy a CD for $1000 that earns 2.5% APR and is compounded quarterly. The CD matures in 5 years. Assume that if funds are withdrawn before the CD matures, the early withdrawal fee is 3 months' interest. What is the early withdrawal fee on this account?

 		A.	$3.75
 		B.	$6.25
 		C.	$3.13
 		D.	$1.25

anywaysss lol @countonme123 

 i tried doing it my way i did it like this

1000+2.5*5-3

tkhunny · Answer

Actually an awesome problem.  One worth investigating.  Oddly, I think there is not a clear solution.  The interest from each quarterly period is different.  Is the penalty the 1st 3 months interest, the last 3 months interest, or otherwise?

The 1st 3 months is 1000*0.025 / 4 = 6.25 - There is an answer there, but I don't necessarily like it.

The total interest that would be earned in the 5 years is 1000(1 + 0.025/4)^{5*4} - 1000 = 132.70.  Then (132.70 / 60)*3 = 6.635 for an AVERAGE three month period.

I think the penalty of the 1st 3 months is being very nice, but that may be the right answer.

Your task now is to figure out why the attempt you provided does not look like any interest formula you ever have seen.

anonymous · Answer

what is the interest formula

tkhunny · Answer

It is given up there in the average interest paragraph.

Amount invested = A
Nominal Interest Rate = i
Compounding periods per year = m
Number of year = n

A(1 + i/m)^(n*m)

In your case, 

A = 1000
i = 0.025
m = 4
n = 5

Giving 1000 (1 + 0.025/4)^(20) for the total accumulation over five year.

However, this was just one speculation on what was meant by the problem statement.  It MAY mean just the first 3 months' interest which is demonstrated above to be 1000 * 0.025/4 = 6.25.

No worries.  With such an odd question, small wonder it left you guessing what the right formula might be.

anonymous · Answer

basically plug them in and solve?

tkhunny · Answer

Personally, I hat the term "plug in", but if you agree that it is the same as "substitution", it will be fine.

anonymous · Answer

oo ok thanks

tkhunny · Answer

The real problem on this one was figuring out what was wanted.  Some formula was the easy part!  Questions should be written better!

anonymous · Answer

yea your right