## jenni_fowler 3 years ago find the amount of money in the bank account given the following conditions: initial deposit= \$5000, annual rate= 3%, time= 2 years

a = initial deposit, r = 1.03, n = 2

3. waheguru

4. jenni_fowler

11th

5. jenni_fowler

says answer is ‎5,304.50

6. GT

It should be 5000 * (1.03)^2. Assuming compounding of the interest rate.

7. jenni_fowler

oh so its 5000(1.03)^2

8. waheguru

Gt where dide u get the 1.3 from

9. GT

At the end of first year, you will have: 5000 + 5000 * 0.03 = 5000 * (1.03). At the end of second year, you will have: 5000 * (1.03) + 5000 * (1.03) * (0.03) Because you earn interest in the second year on the interest amount of the first year. So, that is same as: 5000 * (1.03)^2. In general, for compounded interest, for n years at rate r and principal p, you get: p * (1+r)^n

10. fortheloveofscience

oh yeah compounding of interest... didnt tought of that

11. waheguru

OH

12. waheguru

I GET IT NOW GT TANKS

13. jenni_fowler

so how do i get the answer

14. GT

Use a calculator to find: 5000 * (1.03) * (1.03). That should give you: 5,304.50

15. fortheloveofscience

yup its correct sir

16. jenni_fowler

thanks it swas 5304.5

17. GT

Sometimes, these kind of problems can be formulated such that the interest rate "r" is compounded semi-annually or something else. In that case, the "formula" will be similar, but in that case, in p*(1+r)^n, r represents the rate of interest for that period (semi-annually for example) and n represents the total "compounding" periods.

18. fortheloveofscience

well we all stupidly used simple interest formula..silly me

19. jenni_fowler

so what is the p r and n represent in the equation

20. GT

For example, in this exact same problem, if compounding happened semi-annually, then you will have the following at the end of two years: 5000 * (1+0.015)^4

21. GT

p is initial amount. n is number of periods.

22. GT

r is rate of interest for that period.

23. fortheloveofscience

principle,rate of interest and time period

24. jenni_fowler

so if it were 3000 instead of 5000 and rate was 5.5 and time was 5 years how do i set that up

25. GT

3000 * (1.055)^5

26. fortheloveofscience

use the same algorithm

27. GT

assuming annual compounding.

28. jenni_fowler

ok so its similar to the other one

29. GT

correct.

30. jenni_fowler

i got 3920.88

31. jenni_fowler

rounded

32. GT

Sounds right.

33. jenni_fowler

did i do it right?

34. GT

Yeah, I got the same. :)

35. fortheloveofscience

hmm i guess so..

Oh sorry. My mistake. I gave you the sum formula for geometric progression. The correct formula in this case is: \[a _{n} = ar ^{n-1}\], but in this case, you would take it as \[a _{n} = ar ^{n}\]

37. jenni_fowler

so i did it right :D

38. GT

yes!!

39. jenni_fowler

thakns again everyone

40. fortheloveofscience

say that to GT