Question

Compound interest:
How long does it take a 4000 dollar investment to double if it earns interest at the annual rate of 8%, compounded monthly?

Answer 1

you will want to use your compound formula for this

Answer 2

what are do you have written out as a formula so far?

Answer 3

\[A=P(1+r/n)^nt\]

Answer 4

Sorry that is incorrect
I meant
A=P[1+(r/n)]^nt

Answer 5

good, and since we want to have A = 2P... we can sub it in

divide of the P to start with, then log to reveal the exponent ... then divide off again

Answer 6

2P= P(1+r/n)^nt

2=(1+r/n)^nt

log(2)=nt log(1+r/n)

considering this is just the form:

a = bt, how do we solve for t?

Answer 7

a=bt
t=a/b

Answer 8

yep

a=log(2)

b= n log(1+r/n)

so we know all the parts, therefore we know t

Answer 9

I do not understand

Answer 10

you know that t = a/b ...

and i just defined a and b ... what is not to understand?

Answer 11

Can I just do this:
8000 = 4000[1+(0.08/12)]^12t

Answer 12

that doesnt solve for t tho, but those are the proper placement for the information yes

Answer 13

Then to solve for t i can write:
a=log(2)
b= n log(1+r/n)
t = [log(2)]/[nlog(1+r/n)]
?

Answer 14

yes, after working some algebra to get at 't', we can either work it in a general manner like that; or work the same process but with the specific values in it to start with ... either way.

i prefer the general approach, otherwise we introduce errors when approximating the other values

Answer 15

t= log(2)/(12 log(1+.08/12))

Answer 16

so 8 months, plus part of another, so 9 months if we want to keep it in whole units

Answer 17

years ... that is

Answer 18

I got t = 8.6931

Answer 19

8.69319 years...

8 years and .69319(12) months
8.32

Answer 20

So about 8.32 years

Answer 21

about 8.69 years

more precisely .. 8 years and 8.32 months

Answer 22

Ok makes sense. Thanks

Answer 23

good luck :)