Final answer:
The future value of an investment of $62,300 at a 15.3% annual interest rate compounded continuously for 45 years is approximately $61,214,189.22.
Step-by-step explanation:
To calculate the future value of an investment with continuous compound interest, we use the formula Pert, where P is the principal amount ($62,300), e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate (15.3% or 0.153 as a decimal), and t is the time in years (45 years).
Substituting the given values into the formula, we have:
Future Value = $62,300 * e(0.153 * 45)
Calculating the exponent first:
0.153 * 45 = 6.885
Now raising e to the power of 6.885:
Future Value ≈ $62,300 * e6.885
Future Value ≈ $62,300 * 982.08075197 (using a calculator for e6.885)
Future Value ≈ $61,214,189.22
Therefore, the future value of the investment after 45 years, compounded continuously at 15.3% annual interest, is approximately $61,214,189.22.