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.