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suppose that $36,000 is deposited in an account and the balance increases to $39,786.15 after 2.5 years. how long will it take for the account to grow to $51,806.67? Assume continous compounding

It will take about _ years for $36,000 to grow to $51,806.67

suppose that 36000 is deposited in an account and the balance increases to 3978615 after 25 years how long will it take for the account to grow to 5180667 Assum class=

Respuesta :

mhanifa

Answer:

  • About 9 years

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Continuous compounding equation:

  • [tex]P(t) = P_0e^{rt}[/tex]

Given

  • [tex]P_0=36000[/tex]
  • [tex]P(t)=39.876.15[/tex]
  • [tex]t=2.5[/tex]

Find the value of r

  • [tex]39786.15= 36000*e^{r*2.5}[/tex]
  • [tex]e^{2.5r}=39786.15/36000[/tex]
  • [tex]ln \ e^{2.5r}= ln \ 1.10517[/tex]
  • [tex]2.5r=0.099[/tex]
  • [tex]r=0.099/2.5[/tex]
  • [tex]r=0.04[/tex]

Now find the time t for the balance to grow to $51806.67:

  • [tex]51806.67= 36000*e^{0.04t}[/tex]
  • [tex]51806.67/36000=e^{0.04t}[/tex]
  • [tex]e^{0.04t}= 1.439[/tex]
  • [tex]ln \ e^{0.04t}= ln \ 1.439[/tex]
  • [tex]0.04t=0.3639[/tex]
  • [tex]t=0.3639/0.04[/tex]
  • [tex]t=9.0975[/tex]

The time required is about 9 years.

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