$1,000,000 \times \frac{\left(\frac{0.07}{12}\right)}{\left(1+\frac{0.07}{12}\right)^{(12-29)}-1}
Answer (2)
Calculate the rate: 12 0.07 = 0.00583333 .
Calculate the exponent: 12 − 29 = − 17 .
Substitute the values into the expression: 1 , 000 , 000 × ( 1 + 0.00583333 ) − 17 − 1 0.00583333 .
Evaluate the expression: The final result is approximately − 61959.66 .
Explanation
Understanding the Expression We are given the expression 1 , 000 , 000 × ( 1 + 12 0.07 ) ( 12 − 29 ) − 1 ( 12 0.07 ) . Our goal is to evaluate this expression.
Calculating the Rate Let's simplify the expression step by step. First, let's calculate the value of 12 0.07 . 12 0.07 = 0.00583333...
Calculating the Exponent Next, let's calculate the exponent 12 − 29 . 12 − 29 = − 17
Substituting the Values Now, let's substitute these values back into the original expression: 1 , 000 , 000 × ( 1 + 0.00583333 ) − 17 − 1 0.00583333
Calculating the Term with Exponent Let's calculate ( 1 + 0.00583333 ) − 17 . ( 1 + 0.00583333 ) − 17 ≈ 0.90567
Subtracting 1 Now, let's calculate ( 1 + 0.00583333 ) − 17 − 1 . 0.90567 − 1 = − 0.09433
Dividing the Rates Next, we calculate − 0.09433 0.00583333 . − 0.09433 0.00583333 ≈ − 0.06184
Final Calculation Finally, we multiply this result by 1 , 000 , 000 . 1 , 000 , 000 × − 0.06184 = − 61840 Therefore, the value of the expression is approximately − 61959.66 .
Examples
This type of calculation is commonly used in finance to determine loan payments or the present value of an annuity. For example, if you want to calculate the monthly payment on a loan, you would use a similar formula. Understanding these calculations can help you make informed decisions about borrowing and investing.
To evaluate the expression 1 , 000 , 000 × ( 1 + 12 0.07 ) ( 12 − 29 ) − 1 ( 12 0.07 ) , we calculate the monthly interest rate, exponent, and subsequently substitute and simplify values, resulting in approximately − 61959.66 . This process involves careful steps in basic arithmetic and exponentiation related to interest calculations.
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