Exponential Functions 27

Question

An investment of $1,600 earns 4.6% annual interest, compounded continuously. If no funds are added or removed from this account, what is the future value of the investment after 18 years? (Round your answer to the nearest cent.)

Future Value = $_____

Answer 1

Remember, the formula for compound interest that is compounded continuously is N_final = N_initial * e^(rt), where N_initial is the money you start off with, N_final is the money you have in the end, r is the annual rate expressed as a decimal (so, e.g. 3% would mean r = 0.03), t is the amount of time in years, and e is the mathematical constant e (~2.71828...).

In this case, we have N_initial = 1600, t = 18, and r = 0.046 (4.6% expressed as a decimal). Substituting those terms into the formula, we get N_final = 1600 * e^(0.046 * 18). Performing this calculation on a calculator, we get N_final = 3661.9787. Therefore, our final answer is that the value of the investment will be $3,661.98 after 18 years.