Question

$5000 is invested in an Account which offers 2.125% interest, compounded continuously. How long will it take for the initial investment to double? Round your answer to the nearest year.

a) Approximately 33 years
b) Approximately 25 years
c) Approximately 16 years
d) Approximately 8 years

Answer 1

To calculate how long it will take for an investment to double, we can use the formula for compound interest. In this case, it will take approximately 33 years for the initial investment of $5000 to double at an interest rate of 2.125%, compounded continuously.

Step-by-step explanation:

To determine how long it will take for an investment to double, we can use the formula for compound interest: A = P*e^rt, where A is the final amount, P is the initial investment, r is the interest rate, and t is the time in years. Let's use this formula to solve the problem:

A = 2*5000, P = 5000, r = 2.125/100 = 0.02125

2*5000 = 5000*e^(0.02125*t)

e^(0.02125*t) = 2

Using natural logarithms, we can rewrite the equation as:

0.02125*t = ln(2)

t = ln(2) / 0.02125

t ≈ 32.77

Since we need to round to the nearest year, the answer is approximately 33 years.