Using the continuous compound interest formula, it will take approximately 12.35 years for the initial investment of $5,000 to grow to $100,000 with a 9.7% interest rate compounded continuously. To find out how long it will take for your initial investment to grow to $100,000, we need to use the continuous compound interest formula: A = P*e(rt), where A is the future value, P is the principal amount, e is Euler's number (approximately 2.718), r is the interest rate, and t is the time in years. Substituting the given values, we have 100,000 = 5,000*e(0.097*t). To solve for t, we can divide both sides by 5,000 and take the natural logarithm of both sides. t = ln(100,000/5,000)/0.097 ≈ 12.35 years Using the formula for continuous compounding interest, it will take approximately 12.35 years for a $5,000 investment to grow to $100,000 at an interest rate of 9.7% compounded continuously. Learn more about compound interest here: #SPJ11Final answer:
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