SOLUTION: Find the effective rate of interest for 6% compounded monthly and 6% compounded continuously. First 6% is 0.06 and the equations used are Compounded Continuously {{{A=Pe^rt

Algebra ->  Finance -> SOLUTION: Find the effective rate of interest for 6% compounded monthly and 6% compounded continuously. First 6% is 0.06 and the equations used are Compounded Continuously {{{A=Pe^rt      Log On


   

Question 1102179: Find the effective rate of interest for 6% compounded monthly and 6% compounded continuously.
First 6% is 0.06 and the equations used are
Compounded Continuously
A=Pe%5Ert
Compounded Monthly
A=P%281%2Br%2Fn%29%5Ent

For Monthly I did
A=P%281%2Br%2Fn%29%5Ent
A=P%281%2B0.06%2F12%29%5E12t
and got A=P%281.005%29%5E12t as my answer
For Continuously I did
A=Pe%5Ert
A=100e%5E0.06%281%29
A=+%24106.184
106.184-100=6.184
and got 6.184% as my answer
I just wanted to check if these were ok or if I did steps wrong, thank you!

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you basically find the future value of the present amount of 1 for 1 year at the indicated compounding rate.

you then subtract 1 from that to get the effective interest rate.

your monthly compounding formula is:

A = p * (1 + r/n) ^ nt

A is the future value
p is the present value
r is the interest rate per year
n is the number of compounding periods per year
t is the number of years

with monthly compounding at 6% per year with p = 1 and t = 1, the formula becomes:

A = (1 + .06/12) ^ 12

solve for A to get A = 1.005 ^ 12 = 1.061677812

subtract 1 from A to get effective interest rate = .061677812 per year which is equal to 6.1678812% per year.

your continuous compounding formula is:

A = p * e ^ rt

A is the future value
p is the present value
r is the interest rate per year
t is the number of years

when p = 1 and t = 1 and r = .06, the formula becomes:

A = e ^ .06

solve for A to get A = 1.061836547

subtract 1 from A to get effective interest rate = .061836547 per year which is equal to 6.1836547% per year.

it looks like you did it ok with some minor differences between the way your presented your results and the way i presented mine.

if you're looking for the effective interest rate per year, then t should be equal to 1.

making p equal to 1 allows you to find 1 plus the interest rate.

subtracting 1 from that gets you the interest rate.

i would say you did ok.