financial maths tricky q

Leaving Cert Student

If an individual deposits an amount A monthly for 20 years at interest rate of 6 percent and then wishes to withdraw an amount of 1000 each month for 30 years, how big does A need to be to sustain this?

I have an answer but would appreciate if one of ye could try it and see what ye get first...I feel like I have gone wrong somewhere!

Acciaccatura

Are those 30 years after the 20, or during? And also, is that 6% AER?

Leaving Cert Student

Acciaccatura wrote: »

Are those 30 years after the 20, or during? And also, is that 6% AER?

After and monthly rate

11Charlie11

I'm more than likely way off but I got €330.83

Acciaccatura

11Charlie11 wrote: »

I'm more than likely way off but I got €330.83

Better than what I got, I got 1c :pac: Hang on, let me try again, this'll bug me :P

Edit: I cannot get this at all, sorry . Why the hell am I sitting an honours paper on Friday?

Slow Show

374.15?

You'd get present value of A, then present value of the monthly withdrawals but that's a bit more complicated because they have to start well into the future so the present value of the first withdrawal would be 240 months away (20 years), so yeah you set up your geometric sequence starting at 1000/1.004868^240 and you'd have your 1000 outside the Sn of that sequence, (sorry I'm doing a terrible job of explaining this), then you'd just equate the present value of the deposits with the present value of the withdrawals, you'd only have one variable at this point which would be A.

If anyone needs me to explain that better I'll try!

ahmdoda

i got A equal to 453.0759492$ tell us the answer!!

Undeadfred

Does he deposit at the end of the month or the start?

and does he do the same for the withdrawl?

MathsManiac

Leaving Cert Student wrote: »

After and monthly rate

Monthly rate? Holy crap, that's an AER of over 101%. Where's he managing to get this extraordinary interest rate? Sign me up immediately.

Whatever about the numbers, this sounds very much like the pensions question on the 2012 SEC Phase 3 sample paper. I'm sure you could find a solution to that one on line somewhere.

HPMS

Slow Show is right, it's from the examcraft mock am I correct? And that's the method in the marking scheme. And OP, it's not monthly rate - 6% is the AER. That seems to have caused some confusion too.

Leaving Cert Student

Sorry must have picked it up wrong off teacher... does anyone know if this is solves by equating future values of first 20 years with present values of next 30 in 20 years time? i cant find solution

randylonghorn

Um, just doing a quick calc in my head, and using none of your fancy wancy stuff, I would expect the answer to be over 100k at least.

If he's withdrawing 1,000 per month each month for 30 years, that's 1000 x 12 x 30 = 360,000 he is going to be taking out, so (ignoring any ongoing interest he may receive during those 30 years as the question doesn't mention it), the amount he's left with at the end of the initial 20 years needs to be 360,000.

If he manages that from €300 - 400 of an initial deposit, please point me towards the bank! :pac:


EDIT: ok, just realised that the A is a monthly deposit, not an initial deposit, ignore me completely!!

Slow Show

Leaving Cert Student wrote: »

Sorry must have picked it up wrong off teacher... does anyone know if this is solves by equating future values of first 20 years with present values of next 30 in 20 years time? i cant find solution

I don't really see how it would tbh, can you try to explain your reasoning behind it?

Leaving Cert Student

Well he is making money on his first 20 years of deposits so you want to see how much he will have in 20 years time right?
That would be the future values.

Then at this stage he has to begin withdrawing for thirty years so the present values of the next 30 years at this point would have to equal the total amount of money he has at this point?

By equating them you only have one variable left to solve for... it makes sense to me anyway but financial maths always surprises me so i dunno

Leaving Cert Student

Just tried both methods on a similar q; the one where you equate both present values TODAY, and the one where you equate future value of first 20 and present values of 30 in 20 years time and BOTH work!

0mega

Leaving Cert Student wrote: »

If an individual deposits an amount A monthly for 20 years at interest rate of 6 percent and then wishes to withdraw an amount of 1000 each month for 30 years, how big does A need to be to sustain this?

I have an answer but would appreciate if one of ye could try it and see what ye get first...I feel like I have gone wrong somewhere!

A(1.06)^240 + A(1.06)^239 + A(1.06)^238 + ... + A(1.06)

This is the sum of all your deposits. When you put in the first, it's going to be growing at the 6% interest rate for 240 months. The next month you put in the same amount, but it's only going to be in the account for 239 months and so on..

Take out A so that A[(1.06) + (1.06)^2 + (1.06)^3 + ... + (1.06)^240]

a = (1.06), r = (1.06) and n = 240

Using the geometric series formula, you get: 20920011.15A (this seems ridiculous but a 6% monthly interest rate is very high, are you sure it wasn't the AER and meant to be compounded?)

Anyway, so 20920011.15A is the sum of money that you are going to have in total in 20 years time.

Right, so now he is going to withdraw 1,000 every month for the next 30 years.

So, let's say he started investing money in 2013 and the year is now 2033. So 2033 is now year 0 and 20920011.15A is the present value of the lump sum.

So first month he's going to take out just 1,000 at present value (I'm kinda assuming this not clear from the question. There's also no growth rate of money... I'm just going to take it as 6%?)

So, this series now represents his withdrawals for the next 30 years:

1,000 + 1,000/1.06 + 1,000/1.06^2 + 1,000/1.06^3 + ... 1,000/1.06^359

1,000[1 + 1/1.06 + 1/1.06^2 + 1/1.06^3 + ... 1/1.06^359]

a = 1, r = 1/1.06 and n = 360

So, once again using the geometric series: 1000[17.66666665]

The present value of all his withdrawals: 17,666.67 (Obviously this is not right, as there was no monthly growth rate. I think the method is still right though)

So, the present value of his withdrawals must be equal to the lump sum in his bank account in the year 2033

17,666.67 = 20920011.15A

A = 0.00084448

So he needs to make monthly deposits of that..

Ridiculous obviously, there wasn't enough information in the question but I'm fairly sure that method is right if you can follow it.

ray2012

0mega wrote: »

A(1.06)^240 + A(1.06)^239 + A(1.06)^238 + ... + A(1.06)

This is the sum of all your deposits. When you put in the first, it's going to be growing at the 6% interest rate for 240 months. The next month you put in the same amount, but it's only going to be in the account for 239 months and so on..

Take out A so that A[(1.06) + (1.06)^2 + (1.06)^3 + ... + (1.06)^240]

a = (1.06), r = (1.06) and n = 240

Using the geometric series formula, you get: 20920011.15A (this seems ridiculous but a 6% monthly interest rate is very high, are you sure it wasn't the AER and meant to be compounded?)

Anyway, so 20920011.15A is the sum of money that you are going to have in total in 20 years time.

Right, so now he is going to withdraw 1,000 every month for the next 30 years.

So, let's say he started investing money in 2013 and the year is now 2033. So 2033 is now year 0 and 20920011.15A is the present value of the lump sum.

So first month he's going to take out just 1,000 at present value (I'm kinda assuming this not clear from the question. There's also no growth rate of money... I'm just going to take it as 6%?)

So, this series now represents his withdrawals for the next 30 years:

1,000 + 1,000/1.06 + 1,000/1.06^2 + 1,000/1.06^3 + ... 1,000/1.06^359

1,000[1 + 1/1.06 + 1/1.06^2 + 1/1.06^3 + ... 1/1.06^359]

a = 1, r = 1/1.06 and n = 360

So, once again using the geometric series: 1000[17.66666665]

The present value of all his withdrawals: 17,666.67 (Obviously this is not right, as there was no monthly growth rate. I think the method is still right though)

So, the present value of his withdrawals must be equal to the lump sum in his bank account in the year 2033

17,666.67 = 20920011.15A

A = 0.00084448

So he needs to make monthly deposits of that..

Ridiculous obviously, there wasn't enough information in the question but I'm fairly sure that method is right if you can follow it.

This is exactly why I'm glad that I'm doing ordinary level. :eek:

Acciaccatura

Not related to this particular question, but when they ask "what would be a fair market value for this bond?", what are they looking for? With this question, the bond pays out €5000 at the end of 10 years but also pays €500 at the end of each year for five years. The present values for these €500s add up to €3655.75.

God help me today.

0mega

Acciaccatura wrote: »

Not related to this particular question, but when they ask "what would be a fair market value for this bond?", what are they looking for? With this question, the bond pays out €5000 at the end of 10 years but also pays €500 at the end of each year for five years. The present values for these €500s add up to €3655.75.

God help me today.

Add up the present values of the payments and the original sum.

Acciaccatura

0mega wrote: »

Add up the present values of the payments and the original sum.

So add €2755.37 (present value of the €5000 in 10 years) and the €3655.76 to give a fair market value of anything less that €6411.13? I hope to God I have this right...

0mega

Acciaccatura wrote: »

So add €2755.37 (present value of the €5000 in 10 years) and the €3655.76 to give a fair market value of anything less that €6411.13? I hope to God I have this right...

Yeah

Acciaccatura

0mega wrote: »

Yeah

THERE'S HOPE AFTER ALL! Thank you so much

@OP

@OP, Using an annuity function, I'd say it's
12X * annuity(20 years) := v^20 * 1000 * 12 * annuity(30 years), and assuming the 6% is the annual rate convertible monthly, that's 361 a month
Monthly rate would be 6.16% annual, so v^20 is just (1.0616^-20), and annuity function is just present value of all payments = (1-(1.0616^-20))/.0616 (and replace 20 for 30 for the other side)

That assumes a lot of things though, like the rate, and that it keeps discounting at the same rate when you're withdrawing.
If you insist it's 6% monthly not annually, it'll be about 107.76 a month instead

omega's logic and method look sound enough but using it directly from sequence and series (I suppose you don't do these functions in LC?) maybe trips it up somewhere. I think also you forget the term to bring it to present value allowing for the 20 years of deposits?

Leaving Cert Student

Got it out alright, apologies yet again I misread the question so the info wasn't accurate but I get the method so its cool.

Also, if the rate is 6% per annum compounded quarterly and you invest 1000 how much is it worth at the end of year?

If you mean 6% pa convertible quarterly then 6%/4 = 0.015, (1.015^4) -1 = .0614, * 1000 = answer

Leaving Cert Student

Here is a question: If you borrow €1,000 for one year at an interest rate of 12% per year compounded
quarterly, how much do you owe at the end of the year?

Is the answer 1000(1.12)^4

Leaving Cert Student

Leaving Cert Student wrote: »

Here is a question: If you borrow €1,000 for one year at an interest rate of 12% per year compounded
quarterly, how much do you owe at the end of the year?

Is the answer 1000(1.12)^4

No, what you're doing there is paying 12% each quarter. It'll add up to 57% over the year!
The final rate you should be looking for will be somewhere around the annual rate given, but a bit higher
Do what I did above

Buddy_Paul

I HATE MATHS I TRY BUT NEVER GETT ANY GOOD RESULT

Leaving Cert Student

bluewolf wrote: »

No, what you're doing there is paying 12% each quarter. It'll add up to 57% over the year!
The final rate you should be looking for will be somewhere around the annual rate given, but a bit higher
Do what I did above

This was on one of the mocks marking schemes exactly like I did. Are you telling me they were defiitely wrong?

Leaving Cert Student

Leaving Cert Student wrote: »

This was on one of the mocks marking schemes exactly like I did. Are you telling me they were defiitely wrong?

Your question may be phrased differently, I did say I was making the assumption you meant a convertible rate
What was the exact wording of the question and the exact answer?