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If 4000 dollars is invested in a bank account at an interest rate of 8 per cent per year, Find the amount in the bank after 12 years if interest is compounded annually: Find the amount in the bank after 12 years if interest is compounded quarterly: Find the amount in the bank after 12 years if interest is compounded monthly: Finally, find the amount in the bank after 12 years if interest is compounded continuously:

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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

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