Question

29. How long will it take to double an investment at 3.7% compounded continuously? Round your answer to the nearest tenth of a year. years

Answer 1

The formula for compounding continuously is :

$A=Pe^{rt}$

where A is the future amount

P is the principal amount

e is a constant

r is the rate of interest

and

t is the time in years.

The question stated that the investment will be doubled, so the future amount will be twice the principal amount.

A = 2P

The rate of interest is 3.7%

e is a constant approximately equal to 2.71828..

Subsitute the values to the formula and solve the value of t :

$\begin{gathered} A=Pe^{rt} \\ 2P=Pe^{0.037t} \\ 2=e^{0.037t} \end{gathered}$

Take the natural logarithm of both sides,

note that ln e = 1

$\begin{gathered} \ln 2=\ln e^{0.037t} \\ \ln 2=0.037t\ln e \\ \ln 2=0.037t(1) \\ t=\frac{\ln 2}{0.037}=18.73 \end{gathered}$

The answer is 18.73 years