If 8000 dollars is invested in a bank account at an interest rate of 10 per cent per year,

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Step 1: Convert the interest rate to decimal form:

10% = 0.10

Step 2: Compute the amount in the bank after 11 years if interest is compounded annually:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment) = $8000
r = annual interest rate = 0.10
n = number of times the interest is compounded per year = 1 (since it is compounded annually)
t = number of years = 11

A = 8000(1 + 0.10/1)^(1*11)
A = 8000(1 + 0.10)^11
A = 8000(1.10)^11
A ≈ 23570.18

Therefore, the amount in the bank after 11 years with annual compounding is approximately $23,570.18.

Step 3: Compute the amount in the bank after 11 years if interest is compounded monthly:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment) = $8000
r = annual interest rate = 0.10
n = number of times the interest is compounded per year = 12 (since it is compounded monthly)
t = number of years = 11

A = 8000(1 + 0.10/12)^(12*11)
A = 8000(1 + 0.0083)^132
A ≈ 24046.06

Therefore, the amount in the bank after 11 years with monthly compounding is approximately $24,046.06.

To find the amount in the bank after 11 years with annual compounding, you can use the formula for compound interest:

A = P(1 + r/n)^(n*t)

Where:
A is the final amount in the bank
P is the principal amount (initial investment) ($8000 in this case)
r is the interest rate per period (10% per year, or 0.10)
n is the number of compounding periods per year (1, as interest is compounded annually)
t is the number of years (11 in this case)

Using these values, we can substitute them into the formula to find the answer:

A = 8000(1 + 0.10/1)^(1*11)
A = 8000(1 + 0.10)^11
A = 8000 * 1.1^11
A ≈ $21,589.29

So, if interest is compounded annually, the amount in the bank after 11 years will be approximately $21,589.29.

Now, let's calculate the amount if interest is compounded monthly.

To calculate compound interest with monthly compounding, we need to adjust the formula slightly:

A = P(1 + r/n)^(n*t)

Where:
A is the final amount in the bank
P is the principal amount (initial investment) ($8000 in this case)
r is the interest rate per period (10% per year, or 0.10)
n is the number of compounding periods per year (12, as interest is compounded monthly)
t is the number of years (11 in this case)

Let's substitute these values into the formula:

A = 8000(1 + 0.10/12)^(12*11)
A ≈ $23,668.22

So, if interest is compounded monthly, the amount in the bank after 11 years will be approximately $23,668.22.