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IrinaVladis [17]
3 years ago
11

Annabell invested $2000 into an account earning 3.5% interest compounded continuously. How long will it take to double her inves

tment?
Mathematics
1 answer:
ludmilkaskok [199]3 years ago
5 0

\$2000 will become \$4000 in 19.80 years that is approximately 20 years when compounded continuously at the annual interest rate of 3.5\%

<u>Solution: </u>

Given that  

Amount investe by Annabell = \$2000,

Rate if interest = 3.5\% = 0.035  

Required \ amount = double \ of \ investment = 2\times \$2000 = \$4000

And most important thing that interest is compounded continuously . Formula of Amount where interest is compounded continuously is as follows ,

\mathrm{A}=\mathrm{P} e^{\mathrm{r}{t}}

Where A is final amount,  

P is principal Amount,

r = rate of interest  

And t = duration in years

In our case A = \$4000; \ P = \$2000; \ r = 0.035  

Need to evaluate t that is number of year.

On substituting given values in formula of amount we get

\begin{array}{l}{4000=2000 e^{0.035 t}} \\\\ {=>\frac{4000}{2000}=e^{0.035 t}} \\\\ {\Rightarrow 2=e^{0.035 t}}\end{array}

Taking log both the sides,  

\ln (2)=0.035 \mathrm{t} \times \ln (\mathrm{e})

\Rightarrow \mathrm{t}=\frac{\ln (2)}{0.035}==19.80

That is approximately 20 years.

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