If The Rate Of Inflation Is 4.5%, What Nominal Interest Rate Is Necessary For You To Earn A 3% Real Interest Rate On Your Investment.

[patw1]

If the rate of inflation is 4.5%, what nominal interest rate is necessary for you to earn a 3% real interest rate on your investment.

[factor-fiction]

Is this a coursework question? If so, the answer they may want is 7.635% (since the result of 1.045*1.03 is 1.07635)

[Old_Geezer]

X * I *0.955 = 1.03*X ie reduce by 4.5% inflation yet end up with 3%
I * 0.955 = 1.03
I = 1.03 / 0.955
I = 1.078534031
Therefore return required = 7.8534031%

But I may be wrong.
(Knowing my luck it'll vary depending on whether things are worked out per second or per year.)

[factor-fiction]

I can see OG's way too and initially thought he was right but now I'm not so sure. Certainly both our answers give an answer of slightly above the 7.5% answer.

I look at it like this. Consider an item that costs £100 now. With inflation at 4.5% the same item will cost £104.50 in a year's time.

After a year you will want your £100 to be worth 3% more than the new cost of that item so that you are 3% better off in real terms.

So you want your money to be worth 3% more than £104.50.
That's £104.50 x 1.03 = £107.635

[factor-fiction]

To test OG's approach, suppose inflation was 100% instead of 4.5%. OG's multiplier would have to be 0 (1-1) rather than 0.955 (1-0.05); and this would mean the money had zero value, thus requiring an infinite nominal rate of interest

I think...

[Gizmonster]

I agree with FF's answer - the effect of inflation, is to increase the price by 4.5% (which effectively reduces the price in real terms by 100/104.5).
If you substitute the 0.955 in OG's working and replace it with 100/104.5, we get the same answer as FF =

[Gizmonster]

... damn accidently pressed submit answer, before I'd finished ....

......continued:

If you substitute the 0.955 in OG's working and replace it with 100/104.5, we get the same answer as FF = 1.07635

I don't know why best answer is Methyl's - that's def wrong (sorry!!)

[annominous]

Very interesting discussion for the mathematically-gifted.
So if house prices are rising at 18% in London, how much would they have to rise in a year from today's price to make a 3% profit after 40% tax?

[factor-fiction]

Are you talking about a tax on your profit, annominous?

[Buenchico]

I was going to type out my own answer but then i realised that it would amount to little more than a 'copy & paste' of the excellent response from Factor-Fiction.

So that's a practising maths teacher (Factor-Fiction) and a former one (me) who both make the answer 7.635%. (I've no idea whether Gizmonster has ever taught maths but his reply still counts as yet another vote in favour of that answer!)

[factor-fiction]

Actually I don't think I understand the question at all, annominous- the 18% current figure isn't relevant is it? It depends when you bought it. You need a 5% increase to get a net profit of 3%

[Gizmonster]

You beat me to it FF - I also thought that the figure of 18% is irrelevant.
I agree with the answer of 3% as well, unless I'm misunderstanding the question completely.

... and Buenchico, I've never taught maths - although it was my best subject at school (grade B A level .... although my degree was not in maths).

[Gizmonster]

.... unless annominous means a 3% profit, on top of the 18% increase, after 40% tax ??