Continuous growth (exponential) help!!! THANKS!?

Ok, a bit confused (I wanna get things cleared up for a PRE-test tomorrow)

Ok...

Here%26#039;s some I%26#039;m confused on (practice)

1. At time t in years, the value, V, of an investment of $1000 is given by V=1000e^0.02t. When is the investment worth $3000?

Also,

What is the nominal and effective annual rates for an account paying the stated annual interest, compounded?

3%

a) annually

b) quarterly

c) daily

d) continuously

That one I%26#039;m very confused on:-(

Also,

3. A bank pays interest at the nominal rate of 4.2% per year. What is the effective annual yield if compounding is

a) annual

b) monthly

c) continuous

THANKS SO much

and please show all work so I understand (explanation is good too!)...no magic numbers!!!

Continuous growth (exponential) help!!! THANKS!?online loan

Well as you reposted I guess you want the answers. But remember a pretest is so the teacher can judge what they need to teach you more of and it doesn%26#039;t count towards your marks.

1.

3000 = 1000e^0.02t

divide by 1000

3 = e^0.02t

take log of both sides

log 3 = 0.02t

divide by 0.02

50log3 = t

Type into calculator

t = 54.93

2.

Nominal

a) 3%

b) 3%

c) 3%

d 3%

Effective

E = (1+i/n)^n - 1

a)

E = (1+0.03/1)^1 - 1

E = 3%

b)

E = (1+0.03/4)^4 - 1

E = 3.034%

c)

E = (1+0.03/365)^365 - 1

E = 3.04%

d)

E = e^0.03 - 1

E = 3.045%

3)

Nominal

a) 4.2%

b) 4.2%

c) 4.2%

d 4.2%

Effective

E = (1+i/n)^n - 1

a)

E = (1+0.042/1)^1 - 1

E = 4.2%

b)

E = (1+0.042/12)^4 - 1

E = 4.28%

c)

E = e^0.042 - 1

E = 4.29%

Continuous growth (exponential) help!!! THANKS!?

loan

I can help you with #1.

3000 = 1000e^.02t.

3 = e^.02t

ln 3 = .02t.

t = 54.9 years.

If I knew what nominal and effective annual yields were, I%26#039;d help you with the rest, I promise I would. Sorry. :(