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.Com
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
Compounded Monthly
For Monthly I did
and got as my answer
For Continuously I did
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) (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.
RELATED QUESTIONS
Find the effective rate of interest for 10% compounded... (answered by ikleyn)
Find the effective rate of interest for 7% compounded... (answered by ikleyn)
find the effective rate of interest
10% compounded continuously (answered by Alan3354)
What is the effective rate for an interest rate of 12% compounded... (answered by ikleyn)
1.) What rate (%) compounded quarterly is equivalent to 6% compounded semi-annually?
a. (answered by jim_thompson5910)
A certficate of deposit has an annual rate of 6% compounded quarterly. Find the effective (answered by jojo14344)
Find the effective rate of interest for 8% compounded continuously.
(Round to... (answered by ikleyn)
What is the effective annual rate of investment that pays 6% for 5 yrs compounded... (answered by Boreal)
Find the effective annual interest rate of an account containing $3000 which is... (answered by stanbon)