Question

If you now have $20,184 in your bank account, which has earned 4% interest compounded continuously for 13 years, what was the amount of your original deposit?

A) $15,000
B) $16,000
C) $17,000
D) $18,000

Answer 1

To find the amount of the original deposit, we can use the formula for compound interest: A = P * e^(rt), where A is the final amount, P is the principal (original deposit), e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years. In this case, the original deposit was $15,000.

Step-by-step explanation:

To find the amount of the original deposit, we can use the formula for compound interest: A = P * e^(rt), where A is the final amount, P is the principal (original deposit), e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.

In this case, we have A = $20,184, r = 4% (or 0.04 as a decimal), and t = 13 years. Plugging these values into the formula, we get $20,184 = P * e^(0.04 * 13).

Solving for P, we divide both sides of the equation by e^(0.04 * 13) and find that P = $15,000. Therefore, the amount of the original deposit was $15,000 (option A).