Question

Does 8% annual interest compounded every 6 months mean 8% every 6 months or 4% every 6 months?

Answer 1

Because a year is 12 months...so does 8% annual interest compounded every 6 months get 8% each time or 4% each time (getting 8% at end of year)?

Answer 2

8% interest compounded every 6 months means exactly that - 8% interest, but compounded every 6 months. Number of times compounded per year is unrelated to the interest rate.

Answer 3

Hum. So how would you solve this?

Amy deposited 1,000 into an account that earns 8% annual interest compounded every 6 months. After 6 months, how much will she have.

Answer 4

$1,000 * 1.08?

Answer 5

Or is it 1,000 * 1.04? Sorry for not understand you exactly.

Answer 6

It'd be easier to use the compound interest formula.

Answer 7

Well, I'm not arguing. My GRE book says set it up this way. I cheated and checked the back of the book and it said do it 1,000 * 1.04...

Answer 8

But that formula would be 1,000 (1+ (8/100))^1/2

Answer 9

1000(1+0.08/2)^(2*0.5) would be 1000*1.04, yes

Answer 10

Why did you divide in your formula of compound interest? By book says (1+ (interest/100)) ^time

Answer 11

*divide by 2

Answer 12

Because it's compounded twice a year

Answer 13

Ok. I don't understand, but OK.

Answer 14

\[V=P(1+\frac{ r }{ 100 })^t\]

Answer 15

Look up the compound interest formula

Answer 16

is what my book says is the compound interest formula. You agree?

Answer 17

That formula works too but that assumes compounded once a year.

Answer 18

Ok. Did not know there was more than one formula. I will look it up. Thanks.

Answer 19

ohhh. yeah. I got it now.

Answer 20

I don't know why your book would give that as the formula, but maybe they mean t as the number of time period (ie 6 months would be one time period in this case) and assume you're dividing the r by the number of times compounded per year.

Answer 21

Seems like it'd be easier just to use the actual compound interest formula...

Answer 22

Ok. Let's do it.

Answer 23

\[P ( 1+\frac{ r }{ n })^{nt}\]

Answer 24

Right?

Answer 25

Yes

Answer 26

So, 1,000 (1+ (.08/2))^2*.5

Answer 27

=1,040

Answer 28

That should ne ^(2*.5)

Answer 29

right?

Answer 30

Yes

Answer 31

Ok. Can we do one more for practice?

Bob gets 8% annual interest compounded quarterly, what does he make in 6 months?

Answer 32

That would be the same but with exponent ^(4 * .5) and with the bottom number of the fraction as 4.

Answer 33

Yes

Answer 34

1,040.4

Answer 35

Thanks! That is better than GRE book.

Answer 36

If it asks " what does he make in 6 months?" then i guess they just mean, how much interest earned

Answer 37

Right. Thanks so much!

Answer 38

You're welcome