## anonymous 4 years ago How long will it take for $2000 to double if it is invested at 6.25% interest compounded continuously? can some show me how to set this problem into this equation A=Pe^rt, please! • This Question is Closed 1. Mertsj $4000=2000e ^{.0625t}$ 2. Mertsj $2=e ^{.0625t}$ 3. Mertsj $\ln 2=.0625t(\ln e)$ 4. Mertsj $\frac{\ln2}{.0625}=t$ 5. Mertsj $11.09 yrs = t$ 6. anonymous can you please give me a crash course on what you did, Please... 7. Mertsj Did you understand how the values were substituted into the equation? 8. anonymous no i didnt 9. Mertsj A is the amount which was determined to be$4000 because the problem asked how long it would take a $2000 investment to double. 10. Mertsj If$2000 doubles, it will then be $4000 would you agree? 11. Mertsj So the problem is really asking "how long will it take$2000 to turn into $4000" 12. anonymous what does the e stand for? 13. Mertsj The e is a frequently used mathematical constant. It doesn't stand for anything. It is sort of like pi. Just a commonly used constant. It is part of the formula just like pi is when you write 14. Mertsj $A=\pi r^2$ 15. Mertsj You don't replace pi with anything and you don't replace e with anything. 16. anonymous can you help me figure out another problem but let me do it and maybe you can coach me. 17. Mertsj It's numerical value (if you must know) is 2.718281828... 18. Mertsj ok 19. Mertsj Lay it on me. 20. anonymous What rate of interest compounded continuously is needed for an investment of$500 to grow to \$900 in 10 years?

21. Mertsj

What is A?

22. anonymous

900

23. Mertsj

What is P?

24. anonymous

500

25. Mertsj

What is t?

26. anonymous

10

27. Mertsj

What are you trying to find?

28. anonymous

the rate of interest

29. Mertsj

Yes. r

30. Mertsj

So plug everything in.

31. anonymous

900=500e^r10

32. Mertsj

$900=500e ^{10r}$

33. Mertsj

Divide both sides by 500

34. anonymous

ok

35. anonymous

In1.8=e^10r

36. Mertsj

$1.8=e ^{10r}$

37. Mertsj

Now when you take the natural log of both sides it should look like this: $\ln 1.8=\ln e ^{10r}$

38. anonymous

ok

39. Mertsj

Now bring the exponent down using the third law of logs and get this

40. Mertsj

$\ln 1.8=10r \ln e$

41. Mertsj

But of course ln e = 1 so we have:

42. Mertsj

$\ln 1.8=10r$

43. Mertsj

So just divide both sides by 10 and you are done

44. anonymous

0.18=r

45. Mertsj

$\frac{\ln 1.8}{10}=r=.05878=5.88 %$

46. Mertsj

Did you take the natural log of 1.8 before you divided by 10?

47. anonymous

no

48. Mertsj

Do you now how to do that?

49. anonymous

no

50. Mertsj

You do understand that it says ln 1.8 divided by 10?

51. Mertsj

Do you have a scientific calculator?

52. anonymous

yes

53. Mertsj

Can you find the ln button?

54. Mertsj

It's probably right next to the log button

55. anonymous

yes i just pressed it and got the same as you did do i now dive that by 10

56. Mertsj

Yes

57. Mertsj

Now multiply by 100 to change it to percent.

58. anonymous

got it you just answered my question!! thank you so much Mertsj

59. Mertsj

You're welcome and good luck. Isn't learning fun???!!!

60. anonymous