Question

HELP ME DO THE NATURAL LOG PLEASE!
If Tanisha has $1000 to invest at 6% per annum compounded monthly, how long will it be before she has $1800? If the compound is continuous, how long will it be?

compounding monthly, it will be about __ years before Tanisha has $1800

Compounding continuously, it will be about ___ years before Tanisha has $1800

Answer 1

\[\frac{ 1800 }{ 1000 }= \left( 1+\frac{ 0.06 }{ 365 } \right)^{365 t} \] That is how far as I got. can someone help me do the natural log I alwasy get stuck there

Answer 2

Your equation looks like compounded *daily*

can you change it to compounded monthly ?

Answer 3

opps \[\frac{ 1800 }{ 1000 }= \left( 1+\frac{ 0.06 }{ 12 } \right)^{12 t}\]

Answer 4

next, can you simplify some of those numbers? what is 1+0.06/12 ?
what is 1800/1000 ?

Answer 5

\[\frac{ 9 }{ 5 }=\left( 1.005 \right)^{12 t}\]

Answer 6

ok, but I would use decimals
\[ (1.005)^{12t}= 1.8 \]

now take the log (base 10) or ln (log base e) of both sides (either will work, as long as you use the same base for both sides). Example
\[ \ln\left(1.005^{12t}\right) = \ln(1.8)\]

now use this rule:
\[ \ln(a^b) = b \ln(a) \]
to rewrite the equation as
\[ 12t \ \ln\left(1.005\right) = \ln(1.8)\]

Answer 7

now solve for t by dividing both sides by 12 ln(1.005)
you will need a calculator to find t (in years)

Answer 8

would it be 30.07? if I am doing it right.

Answer 9

I don't get 30.07
what do you get for ln(1.8) ?
then divide by ln(1.005)
then divide by 12

Answer 10

I didnt do ln(1.8) oops . but would you get 9.82. for the continuously it would be the same process. \[1800=1000 e ^{0.06t} \] is how the equation starts.

Answer 11

Yes, 9.821 is what I get for compounding monthly

for compounding continuously, it is the same process
divide both sides by 1000:
\[ e^{0.06t}= 1.8 \]
take the ln of both sides
\[ \ln\left(e^{0.06t}\right)= \ln(1.8) \]
use the same "rule" to get
\[ 0.06t\ \ln(e)= \ln(1.8) \]
now solve for t

(you should not need a calculator to figure out ln(e) is 1)

Answer 12

i got 9.796

Answer 13

yes, very close to compounding monthly.
a difference of about 0.025 years, or 0.3 months or about 9 days faster for continuous compounding

Answer 14

Thank you!!! soo much for helping me with the steps!

Answer 15

yw