You deposit $500 in an account that pays 3% annual interest. Find the balance after 2 years if the interst is compounded with the given frequency.

a) annually
b) quarterly
c) daily

To find the balance after 2 years with different compounding frequencies, we can use the compound interest formula:

A = P(1 + r/n)^(n*t)

Where:
A = the final balance
P = the initial deposit
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years

Let's calculate the balances for each compounding frequency:

a) Annually:
n = 1
r = 3% = 0.03
t = 2
P = $500

A = 500(1 + 0.03/1)^(1*2)
A = 500(1 + 0.03)^2
A = 500(1.03)^2
A ≈ $530.45

The balance after 2 years with annual compounding is approximately $530.45.

b) Quarterly:
n = 4
r = 3% = 0.03
t = 2
P = $500

A = 500(1 + 0.03/4)^(4*2)
A = 500(1 + 0.0075)^8
A ≈ $531.84

The balance after 2 years with quarterly compounding is approximately $531.84.

c) Daily:
n = 365
r = 3% = 0.03
t = 2
P = $500

A = 500(1 + 0.03/365)^(365*2)
A ≈ $531.94

The balance after 2 years with daily compounding is approximately $531.94.

To find the balance after a certain period with different compounding frequencies, you can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final account balance
P = the initial deposit
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years

Let's calculate the balances for each case:

a) Annually compounded:
Given: P = $500, r = 3% = 0.03, n = 1, t = 2

A = 500(1 + 0.03/1)^(1*2)
A = 500(1.03)^2
A ≈ $518.09

The balance after 2 years, with annual compounding, is approximately $518.09.

b) Quarterly compounded:
Given: P = $500, r = 3% = 0.03, n = 4, t = 2

A = 500(1 + 0.03/4)^(4*2)
A = 500(1.0075)^8
A ≈ $518.32

The balance after 2 years, with quarterly compounding, is approximately $518.32.

c) Daily compounded:
Given: P = $500, r = 3% = 0.03, n = 365 (assuming non-leap year), t = 2

A = 500(1 + 0.03/365)^(365*2)
A = 500(1.000082)^(730)
A ≈ $518.36

The balance after 2 years, with daily compounding, is approximately $518.36.

Therefore, the balances after 2 years are:
a) Annual compounding: $518.09
b) Quarterly compounding: $518.32
c) Daily compounding: $518.36

500(1+.03/4) 2*4

500(1+0.085)8 power
500(1.085)8 power
500(8.68) witch equals 4340

I will do b)

amount = 500(1 + .03/4)^(2*4)

http://www.google.ca/#hl=en&source=hp&q=500%281+%2B+.03%2F4%29^%282*4%29&btnG=Google+Search&meta=&aq=f&oq=500%281+%2B+.03%2F4%29^%282*4%29&fp=e8cb7bf60cd4d76c