The cost of attendance at State College is $19,500 for the first year. Devise a periodic savings plan that will allow you to make small deposits for 5 years at a simple interest rate of 1.5% and save enough to pay for the first year at the college.
EP: My comment is NOT directed at you but at the questioner. He/She is asking for 1.5% "simple interest rate", meaning "not compounded". Your formula AND mine are the same and are compound formulas, not "simple interest". Whenever you use "^" in calculating financial problems, you are automatically compounding it. Compounding means you earn " interest on interest", while "simple interest" is just that. You do not earn interest on it.
It is much, much simpler to calculate it, if your interest rate is copounded periodically. You can use this formula to do that: FV=P{[1 + R]^N - 1/ R}. Eample, if you had a monthly plan, the formula would like this: 19,500 = P x {[1 + 0.015/12]^(5*12) -1 / 0.015/12}. Then you would solve for P, or periodic payment. A monthly plan should give you:$313.17.
If you set up a weekly plan, then the weekly payment, using the above formula, would be:$72.23
If you set a daily plan, then the daily payment, using the above formula, would be:$10.29.
+37084 I'm not seeing that as MUCH MUCH simpler than F= A (((1+ i)^(n+1) -1 ) / i )-1) but it gives the same results, so choose whichever one you like ! So many tools.....so few problems....
EP: My comment is NOT directed at you but at the questioner. He/She is asking for 1.5% "simple interest rate", meaning "not compounded". Your formula AND mine are the same and are compound formulas, not "simple interest". Whenever you use "^" in calculating financial problems, you are automatically compounding it. Compounding means you earn " interest on interest", while "simple interest" is just that. You do not earn interest on it.
+37084 Thanks guest ! I understand what you are saying.......
.I felt like giving the YEARLY payment would be closest to avoiding the compounding implications of monthly/weekly etc payments.
+37084 In light of what Guest and I have been discussing, here is the solution with only SIMPLE interest used
the frist year you will deposit 'A' which will get .015 interest for 5 years:
A + A(.015)(5) five years
A + A(.015)(4) four years
A + A(.015)(3) three years
A + A(.015)(2) two years
A + A(.015)(1) one year ALL of these added together need to equal 19500
___________
5A + A(.015)(15)
A(5+(.015)(15))
A(5.225) =19500
A=3732.05 Annual (1st of year) deposit at simple interest of .015
So for simple interest, with annual deposits at the BEGINNING of the year, we can use this equation:
FV = A (n + i \(\sum_{1}^{n}\))
OK......I am done with this question now.....I think !
