- 28 Dec '07 14:12 / 1 editJoe and Mattie, born in 1973, go through college and university, get Phd's, he in lit and her in art. They are very successful, and in 1985, get married. Together they make 400,000 dollars a year, or 240,000 after taxes. Rather than living like millionaires, they decide they will budget their finances to live on 60,000 a year so they sock away 180,000 a year. So in 1986, their first child is born, Alex. Joe writes novels, sells a lot of books every year, and she paints, with her paintings in national galleries. Each year they get a 5% raise so the second year they take home 252,000 and so forth. Every two years another kid is born, first Maria and then Sara. So frst kid in 86, second in 88, third in 1990. So they keep within their 60K budget. It turns out the kids (as well as the parents) have won the intelligence lottery, they all test out at 195 IQ so they will go to college. They slam through school, getting HS diploma's at 13 and at 14 start university. They get scholarships, but only 20,000 and the total tuition, books, housing, cars, etc., comes to 70,000 per year so mom and pop kick in 50,000 a year. The kids, being genius level, go to university for ten years and all three get three separate Phd's in that time, launching very successful carreers in their own right. However, the parents have paid 1.5 MILLION for their three kids education by the time school is finished. The last kid graduated in the year 2014 and the parents want to retire and live off the interest. They have invested at 5% the banked money Which works out to 3 % after taxes. and want to retire after one more big push in 2015 and retire at the beginning of 2016. So how much money per year will they have from the interest on their savings starting in the year 2016?
- 28 Dec '07 16:27 / 2 edits

They both have PhD's and are married at the age of 12? This is simple interest because you dont mention how often it compounded.*Originally posted by sonhouse***Joe and Mattie, born in 1973, go through college and university, get Phd's, he in lit and her in art. They are very successful, and in 1985, get married. Together they make 400,000 dollars a year, or 240,000 after taxes. Rather than living like millionaires, they decide they will budget their finances to live on 60,000 a year so they sock away 180,000 a yea h money per year will they have from the interest on their savings starting in the year 2016?** - 28 Dec '07 17:39

Yeah, they had to have been born in 1963, and it is compound interest, compounded daily as in a normal bank account. I am getting over a nasty cold and my head is not working well right now, full of snot!*Originally posted by joe shmo***They both have PhD's and are married at the age of 12? This is simple interest because you dont mention how often it compounded.** - 28 Dec '07 18:23 / 1 edit

Here it goes*Originally posted by joe shmo***They both have PhD's and are married at the age of 12? This is simple interest because you dont mention how often it compounded.**

I don't have a numerical answer because of the lenghty repetitive calculations. if I understood math a bit better perhaps i would see a shortcut, but perhaps you could tell me if this outline is the way its solved

start with a function to determine there wages after 28 years

f(t) = 240,000(1.05)^t

where (t) is the parents yearly wages at any year (t) starting with 1986

f(0) = 240,000(1.05)^0 = 240,000

f(28) = 240,000(1.05)^28 = about 940,831

next , and this is the part i was to lazy to do.....

I couldn't find any pattern in the series to shorten this up...perhaps you can , i don't know?

sum f(0) through f(28) and subtract 60,000(28) and then subtract 1.5 million from that.......This is the amount you have left to invest after your kids education is paid off ( this is assuming that you saved this money in a piggy bank without it accruing interest the whole 28 years you were saving it. Not a smart move if you ask me, but since the problem doesnt state anthing about compound interest while the money was in the bank, which would make this problem tremendously long i imagine, ill just pretend its not an issue)

then you invest your sum(x) at 3% and after one year youl'll have (1.03x)

if it was compounded daily as you mentioned in you other post

then let X = your principal( what they had left) and use the formula below

X [ 1 + .03/(1/365)^[t ( 1/365)]

t is the the number of years, so if the question is for one year then just pretend it doesn't exist....

I must say in 1986 the Parents must have been quite comfortable, but in 2015 , 60K might be a little less so.....?

i may have overlooked a few things, but i have given it all the time avilable - 28 Dec '07 18:57 / 2 edits

You are missing some factors, for instance, they only live on 60K per year each and every year so its not just the first year they put 180K in the bank. Don't forget they get 5% pay increases too. they also work from 1986 to 2016 so that is a thirty year period. So all the while they are making big bucks they live like me on only 60,000 per year.*Originally posted by joe shmo***Here it goes**

I don't have a numerical answer because of the lenghty repetitive calculations. if I understood math a bit better perhaps i would see a shortcut, but perhaps you could tell me if this outline is the way its solved

start with a function to determine there wages after 28 years

f(t) = 240,000(1.05)^t

where (t) is the parents yearly wa ....?

i may have overlooked a few things, but i have given it all the time avilable

I just had them put the money in a regular savings account for simplicity. If they went to a bond market they might make more money but maybe not. Well I guess technically, they are working only 29 years. So they get interest at 3% after taxes, make it simple interest, compound won't make a huge difference but they get an annual increase of 5% in basic salary, so year #2, they put 192,000 in the band added to the 180,000 plus its interest of 3% So at the end of year 1 they have 185,400 in the bank. They get paid once a year btw. So they start off year two putting 192,000 in the bank and still have 60K to live on. So they start year 2 with 377,400 and at the end of year two they have 388,722. Start of year 3 they get to put 204,600 in the bank so year 3 starts out with 388,722 and at the end of year 3 they have 400,383.66 in the bank. Thats all the farther I have taken it. Not sure of the proper formula for such a situation.

We are talking totally about after tax money here also. They get to do this for 15 years before the first kid goes to college so there will be a lot of money involved. - 28 Dec '07 19:23

Jesus Christ sonhouse, ever hear of the "Enter" key? It splits gigantic paragraphs into more readable chunks. Try it sometime.*Originally posted by sonhouse***You are missing some factors, for instance, they only live on 60K per year each and every year so its not just the first year they put 180K in the bank. Don't forget they get 5% pay increases too. they also work from 1986 to 2016 so that is a thirty year period. So all the while they are making big bucks they live like me on only 60,000 per year.**

I just ha ...[text shortened]... s for 15 years before the first kid goes to college so there will be a lot of money involved. - 28 Dec '07 19:38 / 1 editTo reiterate and to repeat:

family income, paid in full at beginning of year, 400,000 before taxes.

That makes about 240,000 after taxes, they live on 60 and bank the rest,

The bank gives them 5% simple interest, 3% after taxes.

They start their professional life in 1985, have genius kids who are bound for college.

First born, 1986, second 88, third 90.

so they rush through school, get into college at age 14, each one in turn, and go for ten years so they go from year 2000 to year 2014.

The parents pay what the scholarships don't, 50K per year per child.

So total, they pay a cool mil and a half.

Given they get 5% pay increases each year, paid in full at beginning of the year, and the bank gives 5% which becomes 3% after taxes,

what is the interest on the money saved after paying off the kids tuition, they do one year after the last kid graduate and retire on Jan 1 2016. How much money does the interest give them from that day forward? After tax of course.

Each year they manage to live on the 60K plus tuition later, 15 years later. - 28 Dec '07 21:36 / 3 edits

The only way i can see to do this is the way i posted above. You said I missed some factors, but I will attempt to show you that for the most part i haven't missed anything.*Originally posted by sonhouse***To reiterate and to repeat:**

family income, paid in full at beginning of year, 400,000 before taxes.

That makes about 240,000 after taxes, they live on 60 and bank the rest,

The bank gives them 5% simple interest, 3% after taxes.

They start their professional life in 1985, have genius kids who are bound for college.

First born, 1986, second 88, tax of course.

Each year they manage to live on the 60K plus tuition later, 15 years later.

your saying that the first year they have a combined net income of 240,000 dollars, The year is 1986

lets say they banked it all , ill make other deductions later

they are going to bank 29 years of salary

to use the following function we start by letting 1986 = 0

and 2015 = 29

this is because they worked for a year and if they didn't spend anything they have 240,000 banked. But they have 60k for living cost deducted.

From what I gather the bank is giving 3% simple interest after taxes( the 5% is irrelevant )

the first year after interest the make (240,000 - 60,000)(1.03)

At this point they they have 185,400 in the bank , the year is 1986

the next year there wages will increase by 5% and they will again deduct 60 k and the bank will give the 3% interest

there wages for the year (x) after 1986 is represented by the function

g(x) = 240,000(1.05)^x

there wages (x) that they are able to put in the bank use the function

f(x) = x - 60,000

the next function is how much they put in the bank given a 5% increase in wages and deducting 60,000 from that

( f o g )(x) = 240,000(1.05)^x - 60,000

the next function should describe the total amount in the bank at the the end of (x) number of years

we will call it I(x)

I(x) = 1.03{240,000(1.05)^x - 60,000 + [ (f o g)(x-1)(1.03)]}

for clarification purposes i'll plug in some numbers for the year 2015

I(29) = 1.03{240,000(1.05)^29 -60,000 +[ (240,000(1.05)^28 -60,000)(1.03)]}

which eventually simplifies to about

1,835,127.54

deduct 1.5 million from this and you get

335,127.54 in the bank after graduation

you said the bank is going to compound this amount daily at 3%(net)

so the final answer for your total amount in the bank after 2016 should be

335,127.54[1 + .03/ (1/365)]^365

which simplifies to

my calculator can't handle it

please give this a thought, i ve worked on it for quite some time now

if it was compounded quarterly then i come to about $527,329.67

I hope some of the math experts around here check this, cause i don't want to give you a bogus answer!!! - 28 Dec '07 22:06 / 3 edits

Actually I think the idea of this is right, but the end equation is wrong*Originally posted by joe shmo***The only way i can see to do this is the way i posted above. You said I missed some factors, but I will attempt to show you that for the most part i haven't missed anything.**

your saying that the first year they have a combined net income of 240,000 dollars, The year is 1986

lets say they banked it all , ill make other deductions later

they are goin f the math experts around here check this, cause i don't want to give you a bogus answer!!!

It should be like this

I(x)=1.03{240,000(1.05)^(x) -60,000 + [(fog)(x-1)(1.03)] + [(fog)(x-2)(1.03)] +[(fog)(x-3)(1.03)]+............+[ (fog)(x-29)(1.03)]}

i mean for I(3) you wold only calculate down to (fog)(x-3)

just in case people are wondering what i meant

Upon further inspection, I think this is still incorrect? - 28 Dec '07 22:53 / 1 edit

I(3) would be end of year 3? Is there a summation that would do it all at once for a given year? Or are you stuck having to manually do each iteration one at a time?*Originally posted by joe shmo***Actually I think the idea of this is right, but the end equation is wrong**

It should be like this

I(x)=1.03{240,000(1.05)^(x) -60,000 + [(fog)(x-1)(1.03)] + [(fog)(x-2)(1.03)] +[(fog)(x-3)(1.03)]+............+[ (fog)(x-29)(1.03)]}

i mean for I(3) you wold only calculate down to (fog)(x-3)

just in case people are wondering what i meant

It looks like to me even if youleft out any interest or pay increase, 180K per year times 30 would give 5.4 million minus 1.5 mil would still leave 3.9 mil, thats just doing simple multiplication. That looks to me like a reality check, don't you think? - 28 Dec '07 22:56

Like I said....I cant find a summation ( these are pretty daunting numbers to find a pattern)*Originally posted by sonhouse***I(3) would be end of year 3? Is there a summation that would do it all at once for a given year? Or are you stuck having to manually do each iteration one at a time?**

I think it is still slightly incorrect....but i will give it more thought tommarow