Question . Math people, people smarter than me... Everyone....

Plow King

Little bit.
Jesus Christ estimates that by the time he quits work in in 20 years time, he will have accumulated savings of $2.2 million. If the interest rate is 8 % and Jesus will live for 15 years after his retirement because he is taking up extreme irnoning, what annual level of spending will Jesus's savings support under each of the following scenarios:

He wants to die in an extreme ironing accident and leave with $0..

And he wants to leave $500,000 to donate to the extreme ironing fund...

How the F*** do I figure it out?

Compounding annually then divided by the number of years before he gets ironed to death means his yearly expenditure goes up? :S

Please to be helping. :)
 

3viltoast3r

Likes Bikes and Dirt
Ok, this is late, Only interim I will fix it in the morning, this may end up hurting peoples heads but here goes:

ok so we know simple interest formula is P = P0 * (1 + i) right? In this case 1+i = 1.008, P0 = 2.2*10^6

in the first year we have:
P1 = 2.2*10^6*1.008 - payment

We are trying to have a certain payment deducted from each period (1 year) such that, including the inflation, the total sum will be 0.

In the second year, you are going to have the interest compounded from P1, minus the same arbitrary payment. (Here is where I am unsure, does the payment need to have interest as well **will clarifiy in the morning..)

Such that
P2 = P1*1.008 - payment

continuing that
P3 = P2*1.008 - payment
.
.
.
.
Pn = P(n-1)*1.008 - payment
From here you need to formulate a sum ( or series) of all of the terms, Keeping in mind by the end of it all you want to have no monies left over:

So:
P1 + P2 + P3 + ... + P(n-1) + Pn = 0
(zero being your final amount, for the second part set this as 500g)

So from there you should be able to calculate this, remembering to take out common factors to make life alot easier. I will figure out a shorter formula/eqn in the morning for you)

I will fix this in the morning, but it should give you an idea to start off with.



Is this for an assignment? homework? exam?
Something a computer should be doing, rather than by hand..
 

Plow King

Little bit.
It's for a friends assignment. Personally I would just spend the 160k a year and spend the rest on hookers and blow before I die. But then again I'm not Jesus.
 

John U

MTB Precision
What are you going to do when you're resurrected?
Doesn't appear the questions take that into account.
 

thecat

NSWMTB, Central Tableland MBC
It's easier by far to pass a camel through the eye of a needle than for a skint Jesus to tell his dad he blew the plate donations on a party with 12 sailors and a hooker.
 

Robb

Likes Dirt
Standard present value of an annuity (or future value if you wish to take the value to zero as 3viltoast3r suggested).

The concise formula that can be derived is;
PV = CF*(1-(1+i)^(-t))/i

Where CF is the cash flows coming out every year (the unknown in this example), i is your rate (0.08) and t is the number of periods.
for part a) the question isn't clear on when the payments occur, ie at the start of the year (annuity due) or at the end of the year (standard annuity).
At the start of the year would make sense as he plans to live for 15 full years so there is no point in taking money out at the end of the 15th year... this implies that as soon as 20 years is up, he withdraws one payment in full and stops earning interest on it, and he will do this at the start of the next 14 years.

22,000,000 = CF * (1 + ((1-1.08^-14)/0.08))
-> CF = 22,000,000 / (1 + ((1-1.08^-14)/0.08)) = $2,379,861

Part (b) follows on by calculating the present value of the $500,000, deducting it from the $22,000,000 and recalculating the annuity value.
 

Robb

Likes Dirt
hmm, I'm not sure if there is a more simply way.. what is your friend studying?

What that formula is doing is solving for CF/payment in this geometric series
22m = CF + CF*1.08^-1 + CF*1.08^-2 + CF*1.08^-3 + ... + CF*1.08^-14

If you want to avoid using any maths at all, you could set something up in excel and use solver if you have used that before?
 

Langers

Likes Bikes
I had a go at it, I compounded annually with equal payments removed yearly calculated as a geometric series. Sorry about the shitty image and my messy writing/ setting out but I hope it helps you.


Just so you know B is the annual spending and A is the amount left after n years
 
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