Question

Suppose that $2600 is invested at an interest rate of 1.75% per year, compounded continuously. After how many years will the initial investment be doubled? Round your answer to the nearest hundredth.

Answer 1

ANSWER:

39.61 years

STEP-BY-STEP EXPLANATION:

Formula for continous compounding is given by:

$A=P\cdot e^{rt}$

Where,

A = Future Amount: Since investement double = $2600*2 = $5200

P = Principal Amount = $2600

r = Rate of interest = 1.75% = 1.75/100 = 0.0175

t = Time in years = t

Replaicng:

$\begin{gathered} 5200=2600\cdot e^{0.0175\cdot t} \\ \frac{5200}{2600}=e^{0.0175\cdot t} \\ e^{0.0175t}=2 \\ 0.0175t=\ln 2 \\ t=\frac{\ln 2}{0.0175} \\ t=39.608\cong39.61\text{ years} \end{gathered}$

After 39.61 years the initial investment will double