Annuity problem: A college education is expected to cost $20,000/year in 18 years...

donayre21

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I have tried everything so far and can't seem to get the right answer 1450.53 dollars.
I have tried P_o=P[(1-(1+i)^-n)(1+i)]/i and set the answer equals to Pn=P(1+i)^(n)-1/i
where my i=0.10/12 for all cases and n=4*12 for the first equation to find P_o.And n=18*12 for finding P,second equation.Could someone help me out I have been working on this for a few hours.


A college education is expected to cost $20,000 per year in 18 years. Howmuch money should be deposited at the end of each year for 18 years in anaccount earning 10% compounded monthly so that the balance of the accountafter 18 years covers the cost of a college education?
 
A college education is expected to cost $20,000 per year in 18 years. Howmuch money should be deposited at the end of each year for 18 years in anaccount earning 10% compounded monthly so that the balance of the accountafter 18 years covers the cost of a college education?

I have tried everything so far and can't seem to get the right answer 1450.53 dollars.
I have tried P_o=P[(1-(1+i)^-n)(1+i)]/i and set the answer equals to Pn=P(1+i)^(n)-1/i
where my i=0.10/12 for all cases and n=4*12 for the first equation to find P_o.

Erm, sorry but I don't understand what you mean by this. I'll guess you're using 4 years because that's assumed to be the standard length of a college education (although shame on the problem writer for not explicitly specifying; without that assumption, the problem is literally unsolvable). But the problem doesn't state that the cost of a year of college grows at all. Therefore, we can reasonably conclude that the total cost is $20,000/year * 4 years = $80,000.

And n=18*12 for finding P,second equation.Could someone help me out I have been working on this for a few hours.

This sounds like a reasonable path to the solution. The money in the account grows at 10% compounded monthly, for 18 years, so that's a good choice of n. The basic formula for future value is:

\(\displaystyle F = P * (1 + r)^n\)

Where F is the future value, P is the present value, r is the interest rate, and n is number of compounding periods. Plugging in the numbers we know gives us:

\(\displaystyle 80000 = P * \left(1 + \dfrac{0.1}{12} \right)^{216}\)

What happens when you try to solve this equation? Does the answer you get match the given one from the book? Can you compare this tactic to the one you were taking previously and pinpoint where you went wrong before?
 
Erm, sorry but I don't understand what you mean by this. I'll guess you're using 4 years because that's assumed to be the standard length of a college education (although shame on the problem writer for not explicitly specifying; without that assumption, the problem is literally unsolvable). But the problem doesn't state that the cost of a year of college grows at all. Therefore, we can reasonably conclude that the total cost is $20,000/year * 4 years = $80,000.



This sounds like a reasonable path to the solution. The money in the account grows at 10% compounded monthly, for 18 years, so that's a good choice of n. The basic formula for future value is:

\(\displaystyle F = P * (1 + r)^n\)

Where F is the future value, P is the present value, r is the interest rate, and n is number of compounding periods. Plugging in the numbers we know gives us:

\(\displaystyle 80000 = P * \left(1 + \dfrac{0.1}{12} \right)^{216}\)

What happens when you try to solve this equation? Does the answer you get match the given one from the book? Can you compare this tactic to the one you were taking previously and pinpoint where you went wrong before?

The answer is 1450.53 the problem was taking from this book at the end of chapter 4 which is problem 4.9.you could also look at the answer in the back of the book page 286 ftp://nozdr.ru/biblio/kolxo3/F/FM/L...007 i.e. 2006)(ISBN 0387344322)(296s)_FM_.pdf

I really dislike this book it does not give enough detail,any ways I used theorem 4.1 and my teacher told me to use 4.5 "due annuity" but I'm still not getting the right answer.The four years are right for a college education and thank you for the response.
 
Works out this way:
Code:
yr transaction  interest    balance
 1   1450.53         .00    1450.53
 2   1450.53      151.89    3052.95
....
17   1450.53     5686.51   61442.72
18   1450.53     6433.85   69327.10
18 -20000.00         .00   49327.10
19 -20000.00     5165.18   34492.28
20 -20000.00     3611.79   18104.07
21 -20000.00     1895.93        .00
Rate = 10% cpd. monthly = 10.4713% annual
1st deposit at END of year 1
1st withdrawal at END of 18th year
(same time as last deposit!)

Whoever set up that problem should be shot at sunrise!

Could this be done with a simple formula? with out having to take the sum route.Also apparently the author was shot by a student 3 years ago.
 
Who? Clint Eastwood's son?

Can be done with formulas.

PV of immediate annuity:
i = .104713, n = 4, p = 20000
Will give ya 69,327.10

periodic deposit required to reach 69,327.10
i = .104713, n = 18, FV = 69327.10
Will give ya 1,450.53

At the fee you're paying me, I'm not giving
you the formulas: find 'em yerself!

There is something wrong here you are using 18 years for n but the payment is done every month so n=12months*18 years.
I tried doing it including what you told me and got 69737 dollars using the annuity due theorem P_o=P[(1-(1+i)^-n)(1+i)]/i but here is where I get stuck, I used the ordinary annuity theorem Pn=P(1+i)^(n)-1/i which I would want P since I want to know how much I need to put in every month.I have tried it without the months (n=18 i=0.10 P=1529.35) and also with the months (n=18*12 , i=0.10/12 P=116.65) but nothing.From my understanding the second part of the problem should deal with months,why are you dropping them and how did you actually get to the final answer with out including them.
 
Huh? C'mon Don, read YOUR post:

"A college education is expected to cost $20,000 per year in 18 years. How much money should be deposited at the end of each year for 18 years in an account earning 10% compounded monthly so that the balance of the account after 18 years covers the cost of a college education?"

The ONLY mention of month is in "10% cpd. monthly";
that has nothing to do with frequency of deposits.

What I gave you is correct; betya a Canadian loonie...

You are still not being helpful for the second part.
 
I just want to know how you came up with 1450.53 ,after the second part of the problem,since I'm getting 1529.35.What formula did you use since the one I'm using,which applies to this situation,is not working like it should.That is all I want to know,don't get too hung up on the "wrong" part on my post I was questioning you that is why I did it both ways.
 
Last edited:
f = 69,327.10
n = 18 annual deposits of $d
i = .104713
d = annual deposit = ?

d = f*i / [(1 + i)^n - 1] = 1450.530035659073092...:)

Thank you so much for your help so far but here is what I'm working with.I had used this formula in my last post but maybe my calculator(or me.. provably me) is wrong since I keep getting the wrong answer,this is how I'm calculating things:

d= 69,327(0.10)/[(1.10)^(18)-1]=6932.7/4.55991=1520.36

I have been redoing this calculation so much,it has been three days for a problem that has not even been assigned,you can understand how much this is hurting my ego.
 
thank you so much for your help so far but here is what i'm working with.i had used this formula in my last post but maybe my calculator(or me.. Provably me) is wrong since i keep getting the wrong answer,this is how i'm calculating things:

D= 69,327(0.10)/[(1.10)^(18)-1]=6932.7/4.55991=1520.36

i have been redoing this calculation so much,it has been three days for a problem that has not even been assigned,you can understand how much this is hurting my ego.

how in the world are you suppose to know to use 0.104713 when the dam problem tells you it is 10% i will hunt this author down.the answer should be 1520.36
 
d = [69327.10 * .10] / [(1 + .10)^18 - 1] = 1520.3587...

What's wrong with your calculator?

The answer should be 1450.53 in other words you can't use your interest since it is based on using the answer and walking backwards
 
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