$A=35 \times \frac{\left[\left(1+\frac{0.06}{12}\right)^{(12 \cdot 43)}-1\right]}{\left(\frac{0.06}{12}\right)}$
Answer (1)
Calculate the value inside the parenthesis: 1 + 12 0.06 = 1.005 .
Calculate the exponent: 12 ⋅ 43 = 516 .
Calculate the exponential term: ( 1.005 ) 516 ≈ 13.11257 .
Calculate A: A = 35 × 0.005 13.11257 − 1 ≈ 84787.99 .
The final answer is 84787.99 .
Explanation
Understanding the Formula We are given the formula: A = 35 × ( 12 0.06 ) [ ( 1 + 12 0.06 ) ( 12 ⋅ 43 ) − 1 ] Our goal is to calculate the value of A .
Calculate the Inner Parentheses First, we need to calculate the value inside the innermost parentheses: 1 + 12 0.06 = 1 + 0.005 = 1.005
Calculate the Exponent Next, we calculate the exponent: 12 ⋅ 43 = 516
Calculate the Exponential Term Now, we calculate the value of the term with the exponent: ( 1.005 ) 516 ≈ 13.11257
Subtract 1 Subtract 1 from the result of the previous step: 13.11257 − 1 = 12.11257
Calculate the Denominator Calculate the value of the denominator: 12 0.06 = 0.005
Perform the Division Divide the result of step 5 by the result of step 6: 0.005 12.11257 = 2422.514
Multiply by 35 Finally, multiply the result of step 7 by 35: 35 × 2422.514 = 84787.99
Final Answer Therefore, the value of A is approximately 84787.99 .
A ≈ 84787.99
Examples
This formula is commonly used in finance to calculate the future value of an annuity, such as a retirement fund or a savings plan. For instance, if you deposit $35 per period into an account that earns 6% annual interest, compounded monthly, over 43 years, this formula tells you the approximate future value of your investment. Understanding such calculations is crucial for financial planning and investment decisions.
