An investor puts ​$500 in an account that pays 3​% interest compounded annually. Find the account balance after 6 years.

597.026

To find the account balance after 6 years, we can use the formula for compound interest:

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

Where:
A = total amount in the account after the given time period (balance)
P = principal amount (initial investment or deposit)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = number of years

Given:
P = $500
r = 3% = 0.03 (as a decimal)
n = 1 (annually)
t = 6 years

Plugging in the values into the formula, we get:

A = 500(1 + 0.03/1)^(1*6)

Simplifying further:

A = 500(1 + 0.03)^6

Calculating the exponent:

A = 500(1.03)^6

A = 500(1.191016)

A ≈ $595.51

Therefore, the account balance after 6 years will be approximately $595.51.

To find the account balance after 6 years with compounded interest, we can use the formula for compound interest:

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

Where:
A = Final account balance
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years

In this case, the investor puts $500 in the account, the interest rate is 3% (or 0.03 as a decimal), and interest is compounded annually. Thus, we have:

P = $500
r = 0.03
n = 1
t = 6

Substituting these values into the formula, we have:

A = 500(1 + 0.03/1)^(1*6)

Next, we simplify:

A = 500(1 + 0.03)^6

A = 500(1.03)^6

A = 500 * 1.191016

A ≈ $595.51

Therefore, the account balance after 6 years with compounded interest is approximately $595.51.

What is 500(1.03)^6 ?