Question

suppose 8000 is invested at interest rate k, compounded continuously, and grows to 10962.07 in 5 yr. Find the interest rate.

HELLLLPPPP

Answer 1

Using this formula A=P(e)^kt

Answer 2

substitute into this formula: \[A=p(1+\frac{ r }{ n })^{nt}\]

Answer 3

so your p= 8000, a= 10962.07, t=5

Answer 4

ok ill try that

Answer 5

sorry the formula is \[A=pe ^{rt}\]

Answer 6

just substitute and to get the rate out of the exponent do ln on both sides of the equation

Answer 7

dangit i dont know why but im stiil having trouble sorry.. im horrible at word problems

Answer 8

\[10962.07=8000e ^{r5}\]

Answer 9

\[\frac{ 10962.07 }{ 8000 }=e ^{r5}\]

Answer 10

\[137.025875=e ^{r5}\]

Answer 11

i mean i got to that but when i get 1.3703is that the answer or how do i go about the e ^r5

Answer 12

ln both sides

Answer 13

\[\ln 1.37025875=\ln e ^{r5}\]

Answer 14

that will allow to get the r5 out of the exponent:
\[lne=1\]

Answer 15

so do you multiply the 5 by the 1.37025875

Answer 16

divide so that you can isolate r

Answer 17

i got like .27405175

Answer 18

I messed up somewhere, sorry , let me see

Answer 19

okay lol

Answer 20

It should give us the interest rate !

Answer 21

sorry.

Answer 22

are you sure you have the numbers right?. I plug in the wrong numbers all the time. lol

Answer 23

yeah lol

Answer 24

I got it: 6.3%

Answer 25

r=6.3%

Answer 26

since r=0.6299991812 multiplied by 1oo since it's a percentage and rounded out

Answer 27

\[0.06299991812x1000=6.299 \]

Answer 28

6.299=6.3%

Answer 29

if you plug in r in the original equation, it will give you 10962.07, but you have to put that whole crazy number.

Answer 30

OHHHH OK i see

Answer 31

funny, because I have a test tomorrow with these same kind of formulas.

Answer 32

really, i have a test next week

Answer 33

well I hope I helped you out. I learned too at the same time.

Answer 34

haha yea you did thank you. i appreciate your help

Answer 35

sure no problem. I have been helped here by other people too. take care