## toxicsugar22 4 years ago What rate of interstis required so that $1000 will yield$1900 after 5 years if the interset rate is compounded monthly. And I got 12.9% Now How long will it take a sum of money to triple if it is invested at 10% compounded daily

1. heisenberg

there is a formula for this. do you know it / did you use it for the first question?

2. toxicsugar22

yes it is A=P(1+r/n)^nt

3. heisenberg

ok so: r = .10 n = 365 A = 3*P $3*P = P*(1+\frac{.1}{365})^{.1*t}$solve for t.

4. toxicsugar22

so what do we do know

5. toxicsugar22

do i divide by 3

6. heisenberg

well you can start by dividing by P to get rid of it. then you will need to solve for t, which will involve using logarithms.

7. toxicsugar22

so 3=p(1+10/365)^365/t

8. toxicsugar22

is it right

9. heisenberg

no. after dividing by P:$3= (1+\frac{.1}{365})^{.1*t}$

10. heisenberg

then you must use logarithms. I use ln which is log_e, the natural log. $\ln(3)= .1*t*\ln(1+\frac{.1}{365})$ then solve for t.

11. toxicsugar22

ok can you help me do that it really hard for me

12. toxicsugar22

13. heisenberg

so remember, what you do to one side of the equation, you must do to the others. since we want t by itself, we can divide by the other terms to isolate it, like so: $\frac{\ln(3)}{\ln(1+\frac{.1}{365})} = .1*t$ then divide by .1 and you will have t by itself.

14. toxicsugar22

ok can u help more

15. heisenberg

what do you not understand?

16. toxicsugar22

the log

17. toxicsugar22

its so complicated

18. heisenberg

can you use a calculator?

19. toxicsugar22

maybe if you go step by step with me then i will get it

20. toxicsugar22

yes i can use a calc.

21. toxicsugar22

i can but i still need help

22. heisenberg

take the log(3), then divide by the other log. then divide by .1

23. toxicsugar22

ok log 3 is .47712125

24. toxicsugar22

now i divide by what

25. heisenberg

log(1+.1/365)

26. toxicsugar22

i got 1.18968

27. toxicsugar22

is it right

28. toxicsugar22

is it right

29. toxicsugar22

i got .4010500723

30. heisenberg

how did you get 1.18968? you must do the inside of the parentheses first. here is it in an online calculator: http://www.wolframalpha.com/input/?i=log%281%2B.1+%2F+365%29&a=*FunClash.log-_*Log10.Log-

31. toxicsugar22

ok But isnt it .10 instead of .1

32. toxicsugar22

because it wat to know How long will it take a sum of money to triple if it is invested at 10% compounded daily

33. heisenberg

those are the same number! .1 = .10 = .100 = .10000000

34. toxicsugar22

so what is the answere

35. heisenberg

can you not calculate it? it would be better then me just giving it to you.

36. toxicsugar22

i tried

37. toxicsugar22

ut i got a weird answer and im not sure i got it right

38. heisenberg
39. toxicsugar22

it 40104.8

40. toxicsugar22

is that it

41. heisenberg

that doesn't seem right though, heh. does it?

42. toxicsugar22

no it doesnt

43. heisenberg

because i messed up! it is n*t, not r*t. so you should not divide by .1, but by 365

44. toxicsugar22

ok

45. toxicsugar22

so now can u help again

46. heisenberg

you should try and do these yourself on a calculator. you can type it in on this site if you want even. http://www.wolframalpha.com/input/?i=log%283%29+%2F+log%281%2B.1+%2F+365%29+%2F+365&a=*FunClash.log-_*Log10.Log-

47. toxicsugar22

yes

48. toxicsugar22

You do it also and then we will compare aur answers

49. toxicsugar22

okay

50. heisenberg

i just did it. click on that link. it is an online calculator.

51. toxicsugar22

ok i got 10991.6

52. toxicsugar22

is that what you got

53. heisenberg

no. click on the link to see. http://www.wolframalpha.com/input/?i=log%283%29+%2F+log%281%2B.1+%2F+365%29+%2F+365&a=*FunClash.log-_*Log10.Log-

54. toxicsugar22

ok thanks

55. toxicsugar22

im going to give you a medal and be your fan if you be my fan

56. toxicsugar22

do u agree

57. toxicsugar22

u there