On August 8,1981 , American Savings offered an insured tax-free account paying \( 23.24 \% \) compounded monthly. If you had invested \( \$ 50,000 \) at that time, how much would you have on August 8,2014 , assuming that you could have locked the interest rate at the time deposit? Use the formula \[ A=P\left(1+\frac{r}{n}\right)^{n t} \] for \( n=12 \). (Round your answer to the nearest cent.)
Upstudy AI Solution
Answer
Solution
Answered by UpStudy AI and reviewed by a Professional Tutor
Explain 
Simplify this solution Bonus Knowledge
To find out how much you would have on August 8, 2014, using the provided formula, we can plug in the values as follows: - \( P = 50,000 \) - \( r = 0.2324 \) (23.24% expressed as a decimal) - \( n = 12 \) (compounding monthly) - \( t = 33 \) (the number of years from 1981 to 2014) Using the formula: \[ A = P\left(1+\frac{r}{n}\right)^{nt} \] \[ A = 50000\left(1+\frac{0.2324}{12}\right)^{12 \times 33} \] Calculating inside the parentheses: \[ \frac{0.2324}{12} \approx 0.01936667 \] So, \[ 1 + 0.01936667 \approx 1.01936667 \] Now calculate the exponent: \[ 12 \times 33 = 396 \] Now we can compute \( A \): \[ A \approx 50000 \left(1.01936667\right)^{396} \] Using a calculator to find \( (1.01936667)^{396} \): \[ (1.01936667)^{396} \approx 196.1456 \] Finally, calculate \( A \): \[ A \approx 50000 \times 196.1456 \approx 9807281.74 \] Rounding to the nearest cent, the amount you would have on August 8, 2014, is approximately **$9,807,281.74**.
