Final answer:
Cody will have a total of $1,574.81 in his savings account after 3 years, using the compound interest formula with an initial amount of $1,400, an annual interest rate of 4%, and a period of 3 years.
Step-by-step explanation:
The question is about calculating the future value of money in a savings account with compound interest. We know that Cody has a savings account with an initial balance of $1,400 and the account earns a 4% annual interest rate. To find out how much he will have after 3 years, we use the formula for compound interest which is A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
In Cody's case, we are calculating the amount A, with P = $1,400, r = 0.04 (4% interest rate), n = 1 (since it is compounded annually), and t = 3 years.
Substitute these values into the formula to get:
A = 1400(1 + 0.04/1)^(1*3) = 1400(1.04)^3
Now calculate the value of A:
A = 1400(1.04)^3 = 1400 * 1.124864 = $1,574.81
After 3 years, Cody will have a total of $1,574.81 in his savings account.