(1+0.02)(1+0.03) - 1?

Question

the above equation is in my business finance book as an example. it is supposed to represent adding 2% with 3%? the answer is 0.506 which equals 5.06% i dont understand this as i thought 2% + 3% would equal 5%? why is the equation done in brackets and what do the 1's stand for? if anyone can help explain this to me i'd be eternally grateful.

Answer 1

You've misunderstood slightly what it means. What this is doing is increasing something by 2% and then increasing that answer by 3%

The equation is done in brackets to make it clear what order to do things in and which bits go with which.

1+0.02x1+0.03-1 ???? Hard isn't it?

The 1's stand for 100% It's a different way of showing something. For example:

If you wanted to add 10% to 650 you could either work out the 10% (65) and add it on 650+65=715 OR a quicker way is to say you want 110% of the origional figure.

110% means 110 hundreths ie 110/100 = 1.1
650 x 1.1 = 715

Look at your equation. The 1 is the 100% bit (ie 100 hundreths or 100/100) and the 0.02 is the 2 hundredths bit ie 2/100 or 2% (same with the 0.03)

The final 1 is taken away so you get just the increase amount.

Hope this helps

Answer 2

The answer is correct. Stephanie G has shown you the working out so it is left to me to explain how this comes about. Somebody had an intelligent guess about it being something to do with compound interest...and they were right!

The "1" in the first bracket represents 100% so by adding 0.02, we get 1.02. In other words, we have increased its value to 102%. The figures in the second bracket effectively means 103%, so if we multiply this by the figure in the first bracket by the figure in the second bracket (1.02 times 1.03) we get 1.0506. Taking away the "1" outside the bracket takes away 100%, leaving the percentage increase which is 0.0506 or 5.06%. This figure differes from 5% because the 3% has been added to the increased value of 102% not the original value of 100%.

Lets take a practical example:

Suppose you invest £100 in a savings account and you are told that interest is calculated annually at 2%. Then after one year, your account will show you have £102. Now lets assume you get a letter from your bank saying that the interest has increased to 3%. So by the end of the second year, you will have increased your savings by 3%. But this will be a 3% increase on £102 not £100. If you add 3% to £102 you will get £105.06.

Hope this helps!

Answer 3

I don't have any financial background but I can only explain this situation as follows.
When calculating 2% of a number, you multiply the number with 2/100=0.02. For example, if you are trying to calculate 2% interest per month for A amount of money, the equation will be A x 0.02. At the end of the first month you will have (A + 0.02A). A means the 100% of your capital that is 100/100=1. So the equation will be (1+0.02).
If this equation is about calculating something about money, 1's stand for your capital and adding 0.02 means increasing your capital 2% in a period of time.
About your second question: If you put 100 pounds to an account having 2% interest rate, at the end of the first month you will basically have 102 pounds. If you take your money from that bank, take 2 pound of interest you have in your pocket and put 100 pounds again to another bank account having 3% interest rate at the end of the second month you will basically have 103 pounds in hand. As a total you will have 5 pound interest for 100 pounds capital, which means having 5% in total. But if you changed the situation like that: After having 2 pounds of interest for your 100 pounds capital, if you put whole money in an account having 3% interest rate at the end of the second month you will basically have 102 x 0.03 = 105,06 which means 5,06% interest in total. I hope this may help you.

Answer 4

4

Answer 5

If you add what's in the brackets first, then multiply them, then subtract 1 it is .0506, which would be 5.06%. Maybe this represents compound interest or something. The number 1 would represent like $1

Answer 6

Start with X (could be £ or $)
Interest of 2% gives 2 / 100 x X = 0.02X
Now have 1.02X

Interest of 3% gives:-
3/100 x 1.02X
= (3.06/100).X
= 0.0306 X

Now have 1.02X + 0.0306X = 1.0506X

Increase = 0.0506
% increase = 5.06% (as required in answer)

Answer 7

(1+0.02)(1+0.03)-1 = 0.0506 = 5.06%
Brakets means to do/solve what's in there. The answer is probably 5% only because they rounded up 0.0506:
0.0506=
0.051=
0.05=
0.1 ??? I hope this helps you more than me ???

Answer 8

0.506 is correct. You need to multiply, not add. Just break it down step by step...

(1+0.02) = 1.02
(1+0.03) = 1.03
(1.02)(1.03) = 1.506
1.506 - 1 = 0.506

Answer 9

In my book it is an Error.

Answer 10

(1+0.02)
>-1 (-1-0.02)(-1-0.03)-
(1+0.03)

(-1-0.02)(-1-0.03)=(2+0.05)+1