Question

Exponential and logarithmic functions
7.
Calculate the amount of interest earned on $100 in one year at 6% compounded countinuosly. Then determine the exact interest rate in terms of e required to earn the same amount of interest when $100 is deposited in an account where the interest is compounded
a. yearly
b. semi-annually
c. monthly
d. quarterly

Answer 1

formulas given to me:
interest compounded continuously:A=Pe^(rt)
A=P(1+r/n)^(nt)
what I need help with: I'm supposed to express these solutions as a form of e

Answer 2

What I have:I put in the numbers for b, and got
e^0.06=(1+r)^2
0=(1+0.5r)^2-e^0.06
0=(1+0.5r+e^0.03)(1+0.5r-e^0.03)
1+0.5r-e^0.03=0
r=2e^0.03-2
In other words, I used the difference of squares
what everyone else got in my virtual discussion board:
0.0224e
how did they get this answer and what am i doing wrong?

Answer 3

Sigh. Can't even do the beginng of BC calc rite.

Answer 4

you do realize e is just a number right?

e=2.71828...

Answer 5

I know e is a number. But I'm supposed to give this answer in terms of e, just like giving an answer in terms of pi.

Answer 6

(2e^0.03-2) /e = .224

Answer 7

so
r=(2e^0.03-2)=.224e

Answer 8

yaeh but there isn't any point in using e if you are going to approximate in the first place.