Final answer:
The balance in five years with a 4% interest rate compounded annually on a $1,000 investment will grow to $1,216.65, which is more than the original investment.
Step-by-step explanation:
If a person invests $1,000 today in an account with a 4% interest rate, and the interest is compounded annually, we can calculate the future balance using the formula for compound interest, which is A = P(1+r/n)^(nt). Here, 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, and t is the time the money is invested for in years.
In this scenario, the money is invested for five years (t=5), the interest rate is 4% (r=0.04), and we will assume that interest is compounded once per year (n=1). Therefore, we can calculate the future value of the investment as follows:
A = 1000(1 + 0.04/1)^(1*5) = 1000(1.04)^5
After calculating this, we get:
A = 1000 * 1.2166529 = $1,216.65
The balance in five years will indeed be more than the original investment of $1,000.