## 00kirsten 4 years ago How much money would you have to invest to make \$300 within 2 years if the interest rate was 4.5%?

1. BecomeMyFan=D

is it compound or simple interest?

2. 00kirsten

simple interest

3. BecomeMyFan=D

ok, then you have to first know the equation for simple interest, which is I = prt, so I is interest, p ir principal amount invested, r is rate, and t is time, so your equation is 300 = p * (4.5/100) * 2 p is the amount you need to invest to get the interest of 300. and we have to divide the percentage by 100 to get a rate in decimal. so, you simplify and ssubstitute to get: 300 = p * 0.09 p = 300/0.09 p = 3333.33\$ so you got to invest 3333 dollars and 33 cents to get 300\$ interest after 2 years at 4.5% simple interest

4. BecomeMyFan=D

is it clear? do you understand it now?

5. 00kirsten

where did you get the 0.09 from

6. 00kirsten

oh nvm i no how

7. BecomeMyFan=D

well, 300 = p * (4.5/100) * 2 so, if i divide 4.5 by 100 and multiply by 2, I get 0.09

8. BecomeMyFan=D

so all you have to do is remember the formula for simple interest

9. 00kirsten

so how would i write my equation

10. 00kirsten

in all my practice stuff it looks like P = ..... not 300 = p

11. BecomeMyFan=D

ok, the equation for simple interest goes like this: simple interest = amount invested x rate x number of years and dont forget that the rate is in decimal, so if the question gives you a percentage like 4.5% per year, you have to convert it to a decimal rate by dividing the percentage by 100.

12. BecomeMyFan=D

so, after you write down the simple interest formula, you can replace the words with the numbers you are given, and then just solve for the variable you dont know

13. 00kirsten

okay

14. BecomeMyFan=D

get it?

15. BecomeMyFan=D

if, yes, feel free to Become my fan LOL =D

16. 00kirsten

sooo how do i write the equation

17. BecomeMyFan=D

what do you mean??? I already gave you the formula, it can also be writen simply as i=prt so to get the equation, simply replace the letters with numbers, thats it. in your case, it will be like this: \[300 = p * (4.5) * 2\]

18. BecomeMyFan=D

the * is for multiplication =D

19. BecomeMyFan=D

and you can then move the variables around, like this, to make p the subject: \[p = 300/(4.5/100*2)\]

20. BecomeMyFan=D

/ is for division

21. BecomeMyFan=D

and the brackets ( ) simply tell you that you must do the calculations inside them first, before any other calculations

22. 00kirsten

ok thank you...

23. 00kirsten

Calculate the compounded amount on \$2000 for 3 years at 5%, compounded annually.

24. BecomeMyFan=D

wait, so is the 2000 dollars in the question the amount invested ?

25. 00kirsten

i dont no, lol. thats exactly what the question says. i copy and pasted it

26. 00kirsten

i guess so.

27. BecomeMyFan=D

ok, well, this is VERY easy. but since it is compound interest you need to use a different formula, whic is \[A = P(1+R)^{n}\] A is the compound interest PLUS the original amount invested P is the original amount invested R is the rate (dont forget to divide the percentage by 100 to get rate) and n is the number of years so, in your case P is 2000, R is 5%/100=0.05 n is 3, and you do not know the A

28. 00kirsten

ok

29. BecomeMyFan=D

so, \[A = 2000(1+0.05)^{3}\] which is \[A = 2000(1.05)^{3}\] which is A = 2000 * 1.157625 and that results to A = 2315.25 so A is the total amount in bank right now, including both the interest and the original amount, so to get the interest that you got only, you need to subtract the original amount from A, which is 2315.25-2000=315.25 so the compound interest you get after investing a 2000 at 5% compound interest for 3 years is \$2315.25

30. BecomeMyFan=D

got it?

31. BecomeMyFan=D

ok, you know both of the formulas now, and the methods how to solve this kind of problems, so just practise and experiment, and enjoy maths, because maths is EASY if you tell yourelf it is easy, just relax and enjoy it. Good luck. If you got any more questions post them as a new question.

32. 00kirsten

wouldnt it be \$315.25

33. 00kirsten

this is what i did and what i got .... 1year 1 - \$2000 x 0.05 x 1 = \$100 2 year 1 - \$2100 x 0.05 x 1 = \$105 3 year 1 - \$2205 x 0.05 x 1 = \$110.25 100 + 105 + 110.25 = \$315.25

34. BecomeMyFan=D

that is what i said, I just mistakenly forgot to remove the 2 infront

35. BecomeMyFan=D

and that results to A = 2315.25 so A is the total amount in bank right now, including both the interest and the original amount, so to get the interest that you got only, you need to subtract the original amount from A, which is 2315.25-2000=315.25

36. BecomeMyFan=D

A is 2315.25, but this is not interest, it is interest + investment. but interest only is 315.25 so yes you are right

37. 00kirsten

ok thank youuu