## anonymous 5 years ago eresa invested $1425.00 in a savings account at her local bank. the bank pays simple interest of 3.5% annually. how much money would she have in 4 years? • This Question is Closed 1. bahrom7893 is this D.E? 2. bahrom7893 differential equations? 3. anonymous simple interest i guess 4. anonymous i=prt? 5. bahrom7893 oh i dunno i never used that stuff 6. bahrom7893 i think i can do it another way 7. anonymous please show 8. bahrom7893 okay workin on it, afk 9. bahrom7893 let me find a similar problem, i was solving these a couple of weeks ago, will get back to u asap 10. bahrom7893 can u check the answer or do u have the answer? 11. anonymous nopes 12. bahrom7893 k ill do my best 13. bahrom7893 So here I am going to use the following differential equation: dN/dt - k*N = 0 14. bahrom7893 Where N is the amount of money and k is the percent at which it grows. You also know that she invested$1425.00 at some point, so let's call that point the beginning, or time is 0 t = 0

15. bahrom7893

k is given to be 3.5%; so this is what you know: N(0) = 1425.00 (initial value - initial investment is \$1425) dN/dt - 3.5N = 0

16. bahrom7893

Move -3.5N to the right: dN/dt = 3.5N Multiply both sides by dt: dN = 3.5N*dt Divide both sides by N: dN/n = 3.5dt

17. bahrom7893

Integrate both sides: $\int\limits_{}^{}dN/N = \int\limits_{}^{}3.5dt$

18. bahrom7893

on the left side you get: ln|N| + C1= 3.5t + C2, where C1 and C2 are arbitrary constants.

19. bahrom7893

Ln|N| = 3.5t + C2 - C1 (some constant minus another constant is still a constant so ima replace the diff by C3)

20. bahrom7893

Ln|N| = 3.5t + C3. Now I have to get rid of Ln, so we raise e to the both sides of equation: $e^{Ln \left| N \right|} = e^{3.5t+C _{3}}$

21. bahrom7893

are you following me?

22. anonymous

i dont think its that complicated. i am in 6th grade

23. bahrom7893

okay im sure its not that complicated

24. bahrom7893

oh well do u want me to finish it? at least get the answer? I think there def is an easier way using logic or smth, but i have no idea how to solve it that way lol. im in college now

25. anonymous

:-) thanks for your help. you could try

26. bahrom7893

wait i think i messed up somewehere in between

27. bahrom7893

im gettin a ridiculous number

28. anonymous

thats ok...i think it would be: Amount= 1425*(3.5/100)*4

29. bahrom7893

oh crap im using the wrong method. Mine is for changing amount of money, urs is the ez way, they'r assuming that the APR won't change. Like I mean 3.5% of 1425 is not the same as 3.5 of 20k. That's what im solving for, in ur case the 3.5% stays the same.

30. bahrom7893

which means my solution is totally wrong for this problem lol sorry off to help others, but i really cant do this any other way