Help math problem?

Question

A trader takes a loan at 15% compound interest. How many years will it take for the amount to double.

Answer 1

The interest that is compounded continuously (A) = Pe^(rt).

Where,

P is the initial investment

r is the interest rate.

t is time.

In this case,

A = 2P and r = 15% = 15/100 = 0.15.

Substitute the values A = 2P and r = 0.15 in A = Pe^(rt).

2P = Pe^(0.15t)

2 = e^(0.15t)

Take the natural log of both sides.

ln (2) = ln (e^0.15t)

ln (2) = 0.15t

0.6931 = 0.15t

t = 0.6931/0.15 = 4.62.

4.62 years will it take for the ammount to double.