Final answer:
To find out how long it will take for a $5000 investment at 9.7% interest compounded continuously to grow to $100000, the continuous compound interest formula is used, leading to the solution of approximately 15 years.
Step-by-step explanation:
The question asks how long it will take to grow a $5000 investment to $100000 with an account that provides 9.7% interest compounded continuously. To solve for the time, we use the formula for continuous compound interest, which is A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), t is the time in years, and e is the base of the natural logarithm (~2.71828).
First, we need to rearrange the formula to solve for t:
t = ln(A/P)/(r)
Now we can plug in the values:
t = ln(100000/5000)/(0.097)
t = ln(20)/0.097
After calculating the natural logarithm of 20 and dividing by 0.097, we find that t is approximately 15 years.
Therefore, the correct answer is c. 15 years.