+956 Stefania’s parents calculate that they will need $7500 every 3 months for 4 years to pay for Stefania’s college. They have 18 years until she is college age. How much should they invest every 3 months at 6.4%/a compounded quarterly for the next 18 years if they plan to withdraw $7500 per quarter for the 4 years after that?
The Future Value of Stephania's college fund will be =$106,817.02. To save this amount over a period of 18 years or 72 quarters @ 6.4% compounded quarterly, they will need to invest =$787.60 at the beginning of each quarter for 18 years or 72 quarters.
P.S. Do you know or understand the TVM formulas used to calculate these amounts? If you don't, then let us know here and will explain them to you.
+2440 . . . Somehow, I do not believe this reply is from Hectictar
Let’s test the hypothesis by analyzing the presented solution. . . .
Activating super duper computerized analyzing program
(beep . . . beep . . . bong . . . bong . . . bong . . . boink)
Presents the equation(s) ------------------------------Nope
Itemizes the steps --------------------------------------Nope
Annotates the steps in coherent English ---------Nope
Presents the final solution(s) ------------------------Yep
Computerized response:
The presented solution is inconsistent with techniques utilized by Hectictar.
Scanning to identify probable presenter
(beep . . . beep . . . bong . . . boink . . . bink . . . boink . . . boink)
Computer generated answer ------------------------------Yep
Answer soaked in BS ------------------------------------------maybe
Answer coated in thick layer of blarney -----------------Yep
Additional analysis:
Use of blarney instead of work product -----------------Yep
Computerized analysis suggests solution presented by “Blarney bag” or virtual brother, “Blarney banker”
Additional Con Troll notes: “72 Quarters” is equivalent to 18 dollars. Insufficient funds to attend university. Beep . . . Beep . . . Boing
End of Computerized analysis.
Computerized Program ID: Blarney and BS detecting scanning engine version 2.0
by Naus Corps: Con Troll division: Beep . . . Beep . . . Boing .. . Boing . . . Boing
+956 I have all the formula's, but I don't understand how you got the future value
From the point of view of Stefania, it is Present Value of $7,500 quarterly payments, or 16 payments of $7,500 each. For that purpose, you will use this formula:
PV=P{[1 + R]^N - 1.[1 + R]^-N} R^-1 x [1 + R]
PV =7,500 {[1 + 0.064/4]^(4*4) - 1 / [1 + 0.064/4]^(4*4) / (0.064/4)} x [1 + 0.064/4]
PV =7,500{[1.016]^16 -1 / [1.016]^16 / 0.016} x 1.016
PV =7,500 x 14.01798181...... x 1.016
PV =$106,817.02 - This is the PV of Stefania's payments, But it is the Future Value from the point of view of her parents. In other words, this is the amount they must have in future for their daughter's quarterly withdrawals. So, how much do the parents need to invest each quarter to have this amount in 18 years, or 18 x 4 = 72 quarters?
To find that out, you have to use this formula:
FV=P{[1 + R]^N - 1/ R} x [1 + R]
$106,817.02 =PMT {[1 + 0.064/4]^(18*4) - 1 / (0.064/4)} x [1 + 0.064/4]
$106,817.02 =PMT{[1.016]^72 -1 / 0.016} x 1.016
$106,817.02 =PMT x 135.622666.......
PMT =$106,817.02 / 135.622666....
PMT =$787.60 - This is the quarterly payment that her parents must invest at the beginning of each quarter for 18 years or 72 quarters @ 6.4% compounded quarterly.
