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.**

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