Final answer:
To determine the initial investment needed to achieve $17,000 at 5.1% interest compounded continuously after 14 years, use the formula for continuous compounding and rearrange it to solve for the principal. Calculate the exponential factor for the given rate and time, then divide the final amount by this factor to find the principal.
Step-by-step explanation:
To answer the question of how much money needs to be invested at 5.1% interest compounded continuously to have $17,000 after 14 years, we will use the formula for continuous compounding, which is A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal), t is the time in years, and e is the base of the natural logarithm (approximately equal to 2.71828).
To find the initial investment P, we rearrange the formula to get P = A/ert. Plugging in the values given in the question, we get P = 17000/e(0.051*14). Calculating the value of e(0.051*14) and then dividing 17000 by this value will give us the required initial investment.