## inkyvoyd 3 years ago 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

1. inkyvoyd

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

2. inkyvoyd

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?

3. inkyvoyd

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

4. completeidiot

you do realize e is just a number right? e=2.71828...

5. inkyvoyd

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.

6. completeidiot

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

7. completeidiot

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

8. inkyvoyd

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