Question

Suppose $5,400 is invested in an account at an annual interest rate of 3.9% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer:

Answer 1

For interest compounding continuously, we need this formula:

A = Pe^rt

A is Amount at some time t

P is the initial amount

r is the interest rate (as a decimal)

t is number of years

A = 10,800 (since we want the investment to double)

P = 5,400

r = 0.039

A = Pe^rt

10800=5400*e^(0.039*t)

2=e^(0.039*t)

takingnatural logarithmon both sides we get

ln(2)=(0.039*t)ln(e)

t=ln(2)/0.039

t=0.693/0.039

t=17.773 years

t=18 years(rounding to nearest tenth of a year)

It will take 18 years for the investment to double in size.