Find the amount of money in an account after 12 years if $1000 is deposited at 5% annual interest compounded quarterly.
amount = 1000(1 + .05/4)^48
= .....
To find the amount of money in an account after 12 years with a deposit of $1000 at a 5% annual interest rate compounded quarterly, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the initial principal (deposit amount)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Given that P = $1000, r = 5% = 0.05, n = 4 (quarterly), and t = 12, we can substitute these values into the formula:
A = 1000(1 + 0.05/4)^(4*12)
Now, let's simplify the equation step by step:
A = 1000(1 + 0.0125)^(48)
A = 1000(1.0125)^(48)
A = 1000 * 1.8443
A = $1844.30 (rounded to two decimal places)
Therefore, the amount of money in the account after 12 years would be approximately $1844.30.