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November 2nd, 2011, 04:08 AM  #1 
Newbie Joined: Nov 2011 Posts: 7 Thanks: 0  A simple Interest question...or not ?!?
Here is the relevant information: Tim has a daughter, Suzie, who is 12 years old. She wants to go to community collage at 17. Tuition is currently $3000 per year going up 4% a year. Tim decided to setup up a RESP (Canadian Education Savings Plan) for Suzie. He wants to know how much he as to contribute monthly. Here is the question: Approx how much money in nominal dollars will Tim have to set aside each year in his RESP for Suzy to have the funds available for collage when she turns 17? Assume the RESP will earn a nominal rate of 6% So I get that I have to calculate the FV of the cost of tuition 5 years from now. That's a FV calculation. PV = 3000 , I/YR = 4, N = 5 the Future value is 3649.96. The next part is where I'm having a problem. I understand that I have to use the year 1 cost of collage as the PMT value and solve for the PV to figure out the total amount that needs to be saved for by the time Suzie turns 17. So here is what I have so far. PMT = 3649.96 N = 4 FV = 0 I = ??? Here is where I have a problem. The anwser key states that the I/YR is (6  4) ÷1.04 Why is that the I/YR calculation. I don't get it. 
November 2nd, 2011, 05:10 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: A simple Interest question...or not ?!?
You could certainly combine the tuition inflation and the RESP growth rate into a single factor 1.06/1.04 = 1.0192... that would remove the requirement for the first calculation. If you prefer for this to be written as a percent rather than a rate, that's (6%  4%)/1.06.

November 2nd, 2011, 06:32 AM  #3 
Newbie Joined: Nov 2011 Posts: 7 Thanks: 0  Re: A simple Interest question...or not ?!?
But why would I divide by 1.04. Am I missing some basic interest calculation formulas. Everything I've scene is something like (1+r)t. That t is an exponent btw. I have never scene division. Where am I going wrong.

November 2nd, 2011, 06:35 AM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: A simple Interest question...or not ?!?
Could you clarify as to what you're confused about? I gave two formulas, both of which involve division by 1.04. The first one is 'obvious' to me, the second derives from the first (but is lessobvious to me).

November 2nd, 2011, 06:50 AM  #5 
Newbie Joined: Nov 2011 Posts: 7 Thanks: 0  Re: A simple Interest question...or not ?!?
I don't understand the following formula: (62)  1.04 Why are you dividing by 1.04 Thanks. 
November 2nd, 2011, 07:04 AM  #6 
Newbie Joined: Nov 2011 Posts: 7 Thanks: 0  Re: A simple Interest question...or not ?!?
Sorry I mean (64)  1.04 I know 6 is the rate on the resp and the 4 is the inflation on tuition. But I don't understand how the above formula works. 
November 2nd, 2011, 07:27 AM  #7 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: A simple Interest question...or not ?!?
Do you understand the first thing that I wrote, 1.06/1.04?

November 2nd, 2011, 07:43 AM  #8 
Newbie Joined: Nov 2011 Posts: 7 Thanks: 0  Re: A simple Interest question...or not ?!?
Not really.

November 2nd, 2011, 08:04 AM  #9 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: A simple Interest question...or not ?!?
After 5 years the cost will increase from C to 1.04^5 * C. But a fixed amount of money will increase from M to 1.06^5 * M. This can alternatively be expressed as a cost that stays C (so in "2011 dollars", perhaps) and an amount of money that increases to ((1.06^5) / (1.04^5)) * M = (1.06/1.04)^5 * M. That's what the problem expects you to do. But you can use the simple transformation I showed to do this as (6  4)%/1.04 rather than 1.06/1.04  1. I guess finance people see the former as easier or more natural for some reason. 
November 2nd, 2011, 09:34 AM  #10  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: A simple Interest question...or not ?!? Quote:
Like, could you calculate it without a financial calculator? Anyhow, 3649.96 is correct as the tuition fee in 1st year. So year 2 = 3795.96, year 3 = 3947.80, year 4 = 4105.71 : they keep increasing, right? So the problem is finding out how much is required in a 6% account to allow the above 4 annual withdrawals; then finding out the monthly deposit required over 5 years to accumulate to that amount: is that correct?  

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