Question

if something is invested at 6% quarterly, would i multiply 4 to 0.06 of divide 4 by 0.06?

Answer 1

That's compound interest - after the 1st quarter you earn 6% of 100, but after the second quarter you'll earn 6% of 106, and so on.

Answer 2

ye.. its asking me how long it will take for $500 to triple if it is invested at 6% quarterly..

Answer 3

You can use the formula for compound interest, or work it out by hand if it's a small amount. If it's academic I think we'll want to do it the fancy way

Answer 4

So we use
final amount = initial amount * (1 + interest rate) ^ n

Answer 5

where n is how many times you add the interest

Answer 6

yee..

Answer 7

in this case we're looking for n

Answer 8

Yep. Do you know how to get n from there?

Answer 9

well okay so, this is what i did.
A=P(1+r)^t
1500=500(1+0.15)^t
3=(1.015)^t
ln3=tln(1.015)
ln3/ln1.015=t
73.79=t

Answer 10

We can't divide the interest rate by 4. Just use 6%, and then divide t (which will be in 3-month periods) by 4 to get the answer in years.

Answer 11

By the way I rather like the giraffe avatar. I gotta get myself some giraffes of my own.

Answer 12

@jirafa oooh! okay so you're saying i would have to do
A=P(1+r)^t
1500=500(1+0.06)^t/4
3=(1.06)^t/4
ln3=(t/4)ln(1.015)
4ln3/ln1.015=t

Answer 13

lol and yes yes thank you :)

Answer 14

oh my bad... i meant
ln3=(t/4)ln(1.06)
4ln3/ln1.06=t

Answer 15

?:S

Answer 16

There you go!

Answer 17

or would i divide it by 4 after i get t?

Answer 18

Doesn't matter

Answer 19

No, hold on a second

Answer 20

You can either divide by 4 after getting it, or use 4t in the equation

Answer 21

Using t/4 in the equation will convert from years to three month periods, the opposite of what we want

Answer 22

so i would have to work with 1500 = 500 (1.06)^4t

Answer 23

Yep, that's it. I take it that the interest is 6% quarterly, not 6% yearly but compounded quarterly?

Answer 24

If the latter, you need another formula

Answer 25

@Chlorophyll oooh! that works!

Answer 26

@jirafa & @Chlorophyll thanks for your help!

Answer 27

@Chlorophyll so i would do the same if it were compounded daily right?

Answer 28

Yeah, there you go. Should've assumed that the interest rate was annual, that's what everyone and their cat does anyway

Answer 29

Cheers

Answer 30

@jirafa their cats? :S lol

Answer 31

Isn't that a somewhat common English expression? Well nevermind that

Answer 32

Cats certainly can't do compound interest problems, they aren't as smart as giraffes

Answer 33

Later

Answer 34

woah! wait... when i do the daily one... it gives me a huge decimal.. but its like 1.643835616E-4

Answer 35

try it out again, it should work all right

Answer 36

jsut notice that you have to input t as years

Answer 37

not as days

Answer 38

uhh ):

Answer 39

Figured it out already?

Answer 40

yes i did! thankkss :)

Answer 41

how would i solve:

at what rate of interes compounded annually should you invest $500 if you want to have $25000 in 12 years?

Answer 42

@jirafa

Answer 43

Same equation, but this time the variable you need is r

Answer 44

okay. so i got until
ln50=12 ln(1+r)

Answer 45

A=P(1+r)^t
25000=500(1+r)^12
50=(1+r)^12
ln50 = 12 ln (1+r)

Answer 46

Doing alright so far. ln 50 is a number, so calculate that one and divide both sides.

Answer 47

its 3.912=12ln(1+r)
so do i divide3.912 by 12?

Answer 48

I'm unsure if you're correct up to this step:
50=(1+r)^12
If you are, there's no need to take ln!

Answer 49

Yep, there's no unknown in the exponent this time, so we can get rid of it without using ln at all. How would you remove that 12?

Answer 50

um... do ((1+r)^12)^1/12 ? :S

Answer 51

That'll get rid of the 12 all right, but you have to do it in both sides. x^(1/12) = \[\sqrt[12]{x}\] isn't it?

Answer 52

oh okay so
\[\sqrt[12]{50}=\sqrt[12]{(1+r)^{12}}\]

Answer 53

? :s

Answer 54

Right.

Answer 55

YAY! okay thanks so much for your help again @jirafa @Chlorophyll
i shall go to bed now.. its getting late

Answer 56

i got 38.5% btw.

Answer 57

The rate is 38.5 % :0
That's ridiculous rip off !!!

Answer 58

Hah, you definitely need some hardcore interest rate to make 25 grand from $500. By all means do tell me which bank offered you this.

Answer 59

Night