Angela deposits $3000 into an account with an APR of 2.6% for 12 years. Find the future value of the account if interest is compounded monthly. Round your answer to the nearest hundredth, if necessary.
To find the future value of the account with monthly compounding, we use the formula:
FV = P(1 + r/n)^(nt)
where:
FV = future value
P = principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years the money is invested for
In this case, P = $3000, r = 0.026 (2.6% as a decimal), n = 12 (monthly compounding), and t = 12 years.
Plugging in the values, we get:
FV = $3000(1 + 0.026/12)^(12*12)
FV = $3000(1 + 0.00216666667)^144
FV = $3000(1.00216666667)^144
FV = $3000(2.03356901387)
FV = $6101.70
Therefore, the future value of the account after 12 years with monthly compounding is $6101.70.