Consider the following function:𝐴(𝑃,𝑟,𝑛,𝑡)=𝑃(1+𝑟𝑛)𝑛𝑡Where the variables have the following meaning:𝐴 = Amount accumulated 𝑃 = Principal𝑟 = interested 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 = interested 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.)
Solution 1
To find the value of the function A(P,r,n,t) when P=350, r=7.5%, n=12, and t=8, we first need to convert the interest rate from a percentage to a decimal. So, r = 7.5% = 0.075.
Next, we substitute the values into the function:
A = P(1 + r/n)^(nt) A = 350(1 + 0.075/12)^(12*8)
Now, we calculate the value inside the parentheses:
1 + 0.075/12 = 1.00625
Substitute this back into the equation:
A = 350(1.00625)^(12*8)
Now, calculate the exponent:
12*8 = 96
So the equation now is:
A = 350(1.00625)^96
Finally, calculate the value of A:
A ≈ 674.
So, when P=350, r=7.5%, n=12, and t=8, the value of the function A(P,r,n,t) is approximately 674 when rounded to the nearest whole number.
Solution 2
To find the value of the function A(P,r,n,t) when P=350, r=7.5%, n=12, and t=8, we first need to convert the interest rate from a percentage to a decimal. So, r = 7.5/100 = 0.075.
Next, we substitute these values into the function:
A(350, 0.075, 12, 8) = 350(1 + 0.075/12)^(12*8)
Now, we calculate the value inside the parentheses:
1 + 0.075/12 = 1.00625
Substitute this back into the function:
A(350, 0.075, 12, 8) = 350(1.00625)^(12*8)
Now, we calculate the exponent:
12*8 = 96
So, the function becomes:
A(350, 0.075, 12, 8) = 350(1.00625)^96
Finally, we calculate the value of the function:
A(350, 0.075, 12, 8) = 350 * 1.983674897 = 694.286
Rounding to the nearest whole number, we get A(350, 0.075, 12, 8) = 694.
Solution 3
To find the value of the function A(P,r,n,t) when P=350, r=7.5%, n=12, and t=8, we first need to convert the interest rate from a percentage to a decimal. So, r = 7.5/100 = 0.075.
Next, we substitute these values into the function:
A = 350(1 + 0.075/12)^(12*8)
Now, we calculate the value inside the parentheses:
1 + 0.075/12 = 1.00625
Substitute this back into the function:
A = 350(1.00625)^(12*8)
Now, calculate the exponent:
12*8 = 96
So, the function becomes:
A = 350(1.00625)^96
Finally, calculate the value of the function:
A ≈ 697.
So, when P=350, r=7.5%, n=12, and t=8, the value of the function A(P,r,n,t) is approximately 697 when rounded to the nearest whole number.
Similar Questions
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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