Question

How long will it take for an investment to double in valve if it earns 12.25% compounded continuously ?

Answer 1

Answer:

At the given rate it will take 3 years and 5 months for the investment to be doubled

Step-by-step explanation:

Here, we want to get the amount of time it will take an investment that earns 12.25% to double if it’s compounded continuously

We can have the exponential relation as follows;

P = I( 1 + r)^n

P is the present value, let us call this 2x as it two times the initial

I is the initial value which is x in this case

r is the interest rate = 12.25% which is same as 12.25/100 = 0.1225

n is the number of years which we want to calculate

Thus, we have

2x = x( 1 + 0.1225)^n

2 = 1.225^n

Ln 2 = n ln 1.225

n = ln 2/ln 1.225

n = 3.42

if 3.42 is the number of years, let us have 0.42 in months

That will be 0.42 * 12 = 5.04

So we are looking at the investment being doubled at 3 years and 5 months