Final answer:
The balance of a $4000 principal at 5% interest compounded annually over 4 years is $4862.025.
Step-by-step explanation:
To calculate the balance in an account with principal that earns compounded interest, we use the formula A = P(1 + r/n)nt, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), t is the time the money is invested for in years, and n is the number of times that interest is compounded per year.
For this question, the principal P is $4000, the annual interest rate r is 5% or 0.05, the time t is 4 years, and it is compounded annually, so n is 1. Plugging the values into the formula, we get:
A = $4000(1 + 0.05/1)1*4 = $4000(1.05)4 = $4000 * 1.21550625 = $4862.025
The balance in the account after 4 years is $4862.025.