Answer:We can use the formula A = P(1 + r/n)^(nt) to solve this problem, where A is the amount of money in the account after t years, P is the initial investment, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
1. Annual compounding:
A = 4000(1 + 0.08/1)^(1*12)
A = 4000(1.08)^12
A = $10,062.67
2. Quarterly compounding:
A = 4000(1 + 0.08/4)^(4*12)
A = 4000(1.02)^48
A = $10,266.67
3. Monthly compounding:
A = 4000(1 + 0.08/12)^(12*12)
A = 4000(1.0067)^144
A = $10,404.71
4. Continuous compounding:
A = Pe^(rt)
A = 4000e^(0.08*12)
A = $10,491.12
Therefore, the amount in the bank after 12 years if interest is compounded annually is $10,062.67, if it is compounded quarterly is $10,266.67, if it is compounded monthly is $10,404.71, and if it is compounded continuously is $10,491.12.
Step-by-step explanation:I'm just built different