# Financial maths, could you help me out and give me a website with the formulas

• Jul 2nd 2008, 09:34 AM
pitt
Financial maths, could you help me out and give me a website with the formulas
Mr Outov Luk recently emigrated to the UK, bringing with him a painting valued at £250,000. Art experts advised him, however, that it was unlikely to go up in price until the painter died. The painter is only 30, and comes from a very long lived family in the Caucasus. Mr Luk, aged 30 himself, was hoping to use the painting as his pension when he retires at the age of 60.
a) Assuming that the average inflation rate will be 3% per annum for the next 30 years, calculate the present value of Mr Luk’s pension fund.
b) Mr luk decided it was prudent to begin a pension savings plan to top up his pension. He had two options.

Option 1
Invest £200 per month in his company pension plan. The money would be taken from his salary at the end of each month and invested immediately. The company will match his contributions by topping it up by £40 per month. The past performance of the company plan suggests he could get an annual nominal return of 7.2%, compounded monthly on his investment.

Option 2
Make annual lump sum payments into a private pension scheme at the start of each year. Current legislation limits the amount he can put in to £3000 a year. His good friend Mr Nevagivasuka Aneve Nbrake advises him that the scheme run by his company is expected to generate compounded annual nominal returns of at least 10%.

(i) Calculate the value of final pension fund which will be generated by each option.
(ii) In light of your calculations in part i), and of any other considerations which you think might be relevant, what advice would you give to Mr Luk?

Do you mind if you use formulas when resolving it? and if possible could you give me a website that explains how these calculations works so i can understand more? thanks very much
• Jul 3rd 2008, 06:19 AM
TKHunny
a) is kind of hilarious. If you do not specify a discount rate, I suppose we must assume the accumulation rate. If we accumulate and discaount at the same rate, where does that leave us? Are you sure you meant "present" value?

b) Let's see your work. How far have you gotten?
• Jul 3rd 2008, 08:02 AM
pitt
...
Yes i did mean present value

a)PV= fv/(1+r)^n

250000/1.03^30=102997

b(i) calculating the value of the final pension fund which will be generated by each option

option 1

240/ 1.06^12= 119.27

I havent finished yet, but could you just let me know if im on the right track?
• Jul 3rd 2008, 10:01 AM
TKHunny
Why do you have fv = \$250,000? Isn't the painting subject to inflation? If not, then you are good.
• Jul 3rd 2008, 02:39 PM
pitt
..
Quote:

Originally Posted by TKHunny
Why do you have fv = \$250,000? Isn't the painting subject to inflation? If not, then you are good.

The present value of the painting is £102997, which in 30 years time will be worth £250.000. The future value has already been calculated, they were asking me to calculate the present value.

lets go back on this:

option 1

240/ 1.06^12= 119.27

I dont think this is right because i think i had to multiply the number of years (30) times £40= 360. so

240/1.06^360= 1.86 ???

A friend is trying to help me and thats what she said:

Option 1. Payment is monthly so we have 360 periods to consider. The interest rate is 7.2%pa which = 0.6% peer month. The multiple used here is 1.006.

At the end of month 1 we have £240 in the fund.

After month 2 we have 240(1.006) from the first contribution plus another 240.

Month 3 sees 240(1.006)^2 from the first contribution plus 240(1.006) from the second plus 240.

With a bit of manipulation you should see that the formula for the pot at the end is the sum of 240(1.006)^n with n ranging from 0 to 359. Sorry I don't know how to get the maths symbols on here.

p.s. so what do you think, which one is right, mines or hers??
• Jul 4th 2008, 09:09 AM
TKHunny
"bringing with him a painting valued at £250,000. "

Why is that the future value?

That is:

1) The present value,
2) The future value in the absence of inflation, or
3) Both.

If he sold the painting today, you're saying he would get only 102,997 out of it? How does that make sense?

Go with your friend. She seems to have it right on.
• Jul 4th 2008, 10:12 AM
CaptainBlack
Quote:

Originally Posted by pitt
(ii) In light of your calculations in part i), and of any other considerations which you think might be relevant, what advice would you give to Mr Luk?

Sell the painting and put the money in the bank (or rather an investment that pays above the inflation rate - usualy a bank deposit account should do this, but there are better options)

RonL
• Jul 4th 2008, 11:12 AM
pitt
Quote:

Originally Posted by TKHunny
"bringing with him a painting valued at £250,000. "

Why is that the future value?

That is:

1) The present value,
2) The future value in the absence of inflation, or
3) Both.

If he sold the painting today, you're saying he would get only 102,997 out of it? How does that make sense?

Go with your friend. She seems to have it right on.

Ye now i know how to do it, just have one more question

Working out the option 1

240{ [ (1.006)^360 - 1] / 0.006}

which gives 304,614

How do i get the 304,614?? using the calculator, what do i calculate first.. the (1.006)^360-1 and then divide it by 0.006 and then times 240?? its not working out, im not getting 304,614.. i know theres something im doing wrong.. could you just explain how to calculate this on calculator?? thats my last question
• Jul 4th 2008, 12:23 PM
pitt
...
TKhunny dont worry, i know how to do this now.. thanks very much

have you got anything to add up on what captainblack said, about advising Mr luk?? this is not homework by the way, i failed my exam last month and im retaking it in 2 months thats why im here asking questions, i want to fully understand this.. i had 12 out of 100 last month eheh
• Jul 4th 2008, 01:14 PM
TKHunny
1) The painting is not expected to increase in value.
2) Inflation is not 0.
3) The painting is worth less and less and less,
4) One mus choose - Use the 250 now or use the 250 later. If one uses the 250 later, it is worth only 102,997 today.