Not sure where this goes... (wealthy donor paying tuition)

[saint]

Hey- thanks in advance!
Im at such a loss with this problem, I dont know where to begin or end. I tried a few things but I felt i was over complicating things. I was informed theres a formula that applies here and would be highly appreciative to be informed/reminded what it is. The problem is:

A wealthy donor has given MIT $500,000 to be used to pay the tuition of one student every other year until the money
runs out. Under the assumptions that
a. The current annual tuition is $34,986 per year,
b. Tuition goes up at a rate of 4.1%/year, and
c. The principal will be invested so that it earns 5%/year,
How many students will the donation pay for?

 

[Deleted member 4993]

Re: Not sure where this goes...

Hey- thanks in advance!
Im at such a loss with this problem, I dont know where to begin or end. I tried a few things but I felt i was over complicating things. I was informed theres a formula that applies here and would be highly appreciative to be informed/reminded what it is. The problem is:

A wealthy donor has given MIT $500,000 to be used to pay the tuition of one student every other year until the money
runs out. Under the assumptions that
a. The current annual tuition is $34,986 per year,
b. Tuition goes up at a rate of 4.1%/year, and
c. The principal will be invested so that it earns 5%/year,
How many students will the donation pay for?

Since no method was specified - I suggest you set up a spreadsheet and calculate year-by-year. It should be pretty fast.

 

[saint]

Re: Not sure where this goes...

Which would be fine, but I need to know the formula to write a program. :?

 

[Deleted member 4993]

Re: Not sure where this goes...

Which would be fine, but I need to know the formula to write a program. :?

How much money did you start with at the begining of the year ---- A[sub:1o8158un]n[/sub:1o8158un]

How much was college tution -------------------------------------------- T[sub:1o8158un]n[/sub:1o8158un]

How much money left after paying tution............................... (A[sub:1o8158un]n[/sub:1o8158un]-T[sub:1o8158un]n[/sub:1o8158un])

How much money left after drawing interest............................... (A[sub:1o8158un]n[/sub:1o8158un]-T[sub:1o8158un]n[/sub:1o8158un]) * (1.05)^2

Next cycle

How much money did you start with at the begining of the year ---- A[sub:1o8158un]n+2[/sub:1o8158un] = (A[sub:1o8158un]n[/sub:1o8158un]-T[sub:1o8158un]n[/sub:1o8158un]) * (1.05)^2

How much was college tution -------------------------------------------- T[sub:1o8158un]n+2[/sub:1o8158un] = T[sub:1o8158un]n[/sub:1o8158un]*(1.041)^2

How much money left after paying tution............................... (A[sub:1o8158un]n+2[/sub:1o8158un]-T[sub:1o8158un]n+2[/sub:1o8158un])

How much money left after drawing interest............................... (A[sub:1o8158un]n+2[/sub:1o8158un]-T[sub:1o8158un]n+2[/sub:1o8158un]) * (1.05)^2

Now continue this iteration till you get to A[sub:1o8158un]n+2[/sub:1o8158un] < T[sub:1o8158un]n+2[/sub:1o8158un]

______________________

 

[Denis]

Re: Not sure where this goes...

A wealthy donor has given MIT $500,000 to be used to pay the tuition of one student every other year until the money runs out.

CLARIFY that, please. Do you mean every 2 years?
If so, will it start 1 year or 2 years after the $500,000 is invested?

 

[saint]

Re: Not sure where this goes...

The first year I believe is taken out of the principle so: First year,3rd,5th,... etc.

How much money did you start with at the begining of the year ---- A[sub:bcmuu60b]n[/sub:bcmuu60b]
How much was college tution -------------------------------------------- T[sub:bcmuu60b]n[/sub:bcmuu60b]
How much money left after paying tution............................... (A[sub:bcmuu60b]n[/sub:bcmuu60b]-T[sub:bcmuu60b]n[/sub:bcmuu60b])
How much money left after drawing interest............................... (A[sub:bcmuu60b]n[/sub:bcmuu60b]-T[sub:bcmuu60b]n[/sub:bcmuu60b]) * (1.05)^2
Next cycle
How much money did you start with at the begining of the year ---- A[sub:bcmuu60b]n+2[/sub:bcmuu60b] = (A[sub:bcmuu60b]n[/sub:bcmuu60b]-T[sub:bcmuu60b]n[/sub:bcmuu60b]) * (1.05)^2
How much was college tution -------------------------------------------- T[sub:bcmuu60b]n+2[/sub:bcmuu60b] = T[sub:bcmuu60b]n[/sub:bcmuu60b]*(1.041)^2
How much money left after paying tution............................... (A[sub:bcmuu60b]n+2[/sub:bcmuu60b]-T[sub:bcmuu60b]n+2[/sub:bcmuu60b])
How much money left after drawing interest............................... (A[sub:bcmuu60b]n+2[/sub:bcmuu60b]-T[sub:bcmuu60b]n+2[/sub:bcmuu60b]) * (1.05)^2
Now continue this iteration till you get to A[sub:bcmuu60b]n+2[/sub:bcmuu60b] < T[sub:bcmuu60b]n+2[/sub:bcmuu60b]
______________________

Im gonna take your word for it! THANK YOU!

 

[Denis]

Re: Not sure where this goes...

How much money did you start with at the begining of the year ---- A[sub:15x5g1ww]n[/sub:15x5g1ww]

How much was college tution -------------------------------------------- T[sub:15x5g1ww]n[/sub:15x5g1ww]

How much money left after paying tution............................... (A[sub:15x5g1ww]n[/sub:15x5g1ww]-T[sub:15x5g1ww]n[/sub:15x5g1ww])

How much money left after drawing interest............................... (A[sub:15x5g1ww]n[/sub:15x5g1ww]-T[sub:15x5g1ww]n[/sub:15x5g1ww]) * (1.05)^2

Subhotosh, shouldn't the interest be calculated on the beginning balance?

A simple program can handle it:
a = 500000
t = 34986
DOWHILE a>t
s = s+1 : students helped
t = t * (1.041)^2 : calculate tuition
a = a * (1.05)^2 : add interest
a = a - t : deduct tuition
PRINT s, t, a

 

[Deleted member 4993]

Re: Not sure where this goes...

How much money did you start with at the begining of the year ---- A[sub:31qpgl5o]n[/sub:31qpgl5o]

How much was college tution -------------------------------------------- T[sub:31qpgl5o]n[/sub:31qpgl5o]

How much money left after paying tution............................... (A[sub:31qpgl5o]n[/sub:31qpgl5o]-T[sub:31qpgl5o]n[/sub:31qpgl5o])

How much money left after drawing interest............................... (A[sub:31qpgl5o]n[/sub:31qpgl5o]-T[sub:31qpgl5o]n[/sub:31qpgl5o]) * (1.05)^2

Subhotosh, shouldn't the interest be calculated on the beginning balance?

My interpretation of the problem was that - we start with some money at the begining of the year - pay-off tution in the begining of the year - the money sits there (after tution) for two years earning interest - and the cycle continues.....
A simple program can handle it:
a = 500000
t = 34986
DOWHILE a>t
s = s+1 : students helped
t = t * (1.041)^2 : calculate tuition
a = a * (1.05)^2 : add interest
a = a - t : deduct tuition
PRINT s, t, a

 

[Denis]

Re: Not sure where this goes...

My interpretation of the problem was that - we start with some money at the begining of the year - pay-off tution in the begining of the year - the money sits there (after tution) for two years earning interest - and the cycle continues.....

Ahhh...I see. So you could start with students=1, start = 500000 - 34986; then go man go every 2 years; mais oui?

a = 500000 - 34986
t = 34986
s = 1
DOWHILE a>t
s = s+1 : students helped
t = t * (1.041)^2 : calculate tuition
a = a * (1.05)^2 : add interest
a = a - t : deduct tuition
PRINT s, t, a

 

[saint]

Ok, I used:
Code:---------------------------------------------------------------------------------------------------------------
A[sub:16h4xi40]n[/sub:16h4xi40] = 500000
T[sub:16h4xi40]n[/sub:16h4xi40] = 34986
A[sub:16h4xi40]n+2[/sub:16h4xi40] = 1
T[sub:16h4xi40]n+2[/sub:16h4xi40] = 0
S = 0

while A[sub:16h4xi40]N+2[/sub:16h4xi40] > T[sub:16h4xi40]n+2[/sub:16h4xi40]:
S += 1
A[sub:16h4xi40]n[/sub:16h4xi40] = A[sub:16h4xi40]n[/sub:16h4xi40] - T[sub:16h4xi40]n[/sub:16h4xi40]
A[sub:16h4xi40]n+2[/sub:16h4xi40] = A[sub:16h4xi40]n[/sub:16h4xi40] - T[sub:16h4xi40]n[/sub:16h4xi40] * ( 1.05**2)
T[sub:16h4xi40]n[/sub:16h4xi40] = T[sub:16h4xi40]n[/sub:16h4xi40] * ( 1.041**2)
T[sub:16h4xi40]n+2[/sub:16h4xi40] = T[sub:16h4xi40]n[/sub:16h4xi40]
A[sub:16h4xi40]n+2[/sub:16h4xi40] = A[sub:16h4xi40]n+2[/sub:16h4xi40] - T[sub:16h4xi40]n+2[/sub:16h4xi40]
A[sub:16h4xi40]n+2[/sub:16h4xi40] = A[sub:16h4xi40]n+2[/sub:16h4xi40] * ( 1.05**2)
print A[sub:16h4xi40]n+2[/sub:16h4xi40], '\t', T[sub:16h4xi40]n+2[/sub:16h4xi40], '\t', S
/Code---------------------------------------------------------------------------------------------------------------

Which gives me:

Output:-------------------------------------------------------------------------------------------------------------
428352.419366 . . . 37913.663466 . . . 1
379496.161921 . . . 41086.3167385 . . . 2
326551.563997 . . . 44524.4608095 . . . 3
269176.509174 . . . 48250.3122145 . . . 4
207000.252388 . . . 52287.9465909 . . . 5
139621.024258 . . . 56663.4542496 . . . 6
66603.434939 . . . 61405.1087646 . . . 7
-12524.3392719 . . . 66543.5496712 . . . 8
/Output------------------------------------------------------------------------------------------------------------

But I double checked it with a spread sheet:
http://spreadsheets.google.com/ccc?key= ... xHfw&hl=en

and got twice the number of students paid for- where did I go wrong or what did I miss?

EDIT: I fixed the problem. Thanks.
while An2 > Tn2:
s += 1
An = An - Tn
An = An * (1.05**2)
Tn = Tn * (1.041**2)
An2 = An
Tn2 = Tn
An2 = An2 - Tn2

Returns 15- which is correct.