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Consider the following function:A(P,r,n,t)=P(1+rn )ntWhere the variables have the following meaning:A = Amount accumulated P = Principalr = interest rate n = compounding per period t = number of periods Find the value of the function when P=350, r=7.5%, n=12, and t=8.(Round your answer to the nearest whole number.)

Question

Consider the following function:A(P,r,n,t)=P(1+rn )ntWhere the variables have the following meaning:A = Amount accumulated P = Principalr = interest rate n = compounding per period t = number of periods Find the value of the function when P=350, r=7.5%, n=12, and t=8.(Round your answer to the nearest whole number.)

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Solution

To find the value of the function A(P,r,n,t)=P(1+rn)^(nt) when P=350, r=7.5%, n=12, and t=8, follow these steps:

  1. Convert the interest rate from a percentage to a decimal. So, r = 7.5% = 0.075.

  2. Substitute the values into the function:

    A(350, 0.075, 12, 8) = 350(1 + 0.075/12)^(12*8)

  3. Simplify the expression inside the parentheses:

    = 350(1 + 0.00625)^(96)

  4. Calculate the value inside the parentheses:

    = 350(1.00625)^(96)

  5. Raise 1.00625 to the power of 96:

    = 350 * 1.8163

  6. Multiply 350 by 1.8163 to get the final answer:

    = 635.205

Rounding to the nearest whole number, the value of the function A when P=350, r=7.5%, n=12, and t=8 is approximately 635.

This problem has been solved

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