Compound Interest calculation on savings...

Ad · 2011-03-17 07:46:45

Last ditch attempt them. As I understand it a root is a number multiplied by its to reach another number.

2 is the 4th root of 16 or 2x2x2x2=16. Which is different to 16/4=4 or 4+4+4+4=16. I understand the difference. What I don't understand is why interest is calculated that way. Is it so the banks make more money on debts and pay less on savings?

I don't know how you find the root when you are give a random number.

My first instinct is to share it by the number you're give ie the 12th root of 12 at first glance for me would be 1 but 1x1x1x1x1x1x1x1x1x1x1x1=1 so without a calculator what would you do? PS I know its 1.23...etc.

Bob · 2011-03-28 19:49:36

hi Ad,

Sorry for the delay replying. I've been away on holiday in Egypt!

I'm just catching up on all my mail etc. I'll have a go at a reply later today. If you read this please give a quick post back so I know you're awaiting my longer response.

Bob

Bob · 2011-03-28 22:42:38

hi Ad,

Let's start with some basics.

You thought £38 was not great for the savings account.

But, if you put £1200 in a savings account for a full year at 6% you'd get 1200 x 6 / 100 = £72.

But you are not giving them all the money at the start; they get it a bit at a time. £38 is better than half of 72 so I think it's not bad. Remember, rates are really low in the UK at the moment, so that's about as good as it will get unless you risk the markets or the horses.

Now for multipliers.

If you wanted to work out lots of 6% interest amounts the quickest way would be like this:

x 6 / 100 = 0.06.

So use 0.06 as a multiplier.

eg. £1200 x 0.06 = £72.

The multiplier gets the answer in one step.

If you want to know the new amount in the account then you would add the old amount and the interest.

But the use of a multiplier makes this quick too.

I want 100% of the old amount and another 6% of the old amount. That's 106% altogether.

So use x 1.06 as the multiplier for this.

eg . £1200 x 1.06 = £1272.

You won't get the answers any quicker than that; just one multiplication and it's done!

Now let's suppose you leave the money in the account for another year.

£1272 x 1.06 = £1348.32

You can go on like this for year after year getting the new amounts with just one multiplication for each year.

This way for calculating interest is called compound interest. Notice that the interest for the second year is more than the first year because you are starting with a larger amount this time. Or to think of it another way, you get interest on the interest.

Now for the monthly multipliers.

Banks are required by law to give yearly interest rates but they may choose to give monthly ones too.

This certainly happens for credit cards. I've just had a look at Barclaycard's rates and they state:

monthly rate = 1.313%

http://www.barclays.co.uk/Creditcards/PurchaseCreditCards/H1242558463459?selectedGroupName=PurchaseCreditCards

Now if you owed some money on your credit card and didn't pay off anything at all, then the debt would get bigger every month by that rate. But Barclays must say what the yearly rate is.

So they get the multiplier ( 1.01313) and multiply it by itself 12 times over:

x 1.01313 x 1.01313 x 1.01313 x 1.01313 x 1.01313 x 1.01313 x 1.01313 x 1.01313 x 1.01313 x 1.01313x 1.01313 x 1.01313 = 1.169451 (I suggest you try this yourself; it'll help you to see what happens)

So they quote the APR (= annual percentage rate) as 16.9%

Now I cannot think of another way to change from monthly to yearly or back the other way. You have to use multipliers because calculators and computers have functions that allow us to do the calculation that way. [Anyone else reading this .... if there is another way, I'd be interested in knowing what it is]

Now you are right that roots are involved in these calculations

If you just did 1.01313 x 12 = 12.15756 you would not get the right APR! It's not even close. Barclays would get into all sorts of trouble if they used that figure.

Why must you multiply the multipliers rather than adding up 12 of them?

Because each month the credit card company looks at what you owe and calculates the interest on that ... so you pay interest on the interest .... it's compound interest again.

At the bottom I've put a graph. I wanted to start with £100 and add on monthly interest. At the end of the year I wanted to end up with £106.

The figures above the graph show that happening.

If I had done 6% divided by 12 = 0.5% I would not have got to £106

After 12 monthly calculations of 0.5% per month you get £106.1678. It's come out to more because of all the interest on the interest ... a few extra pennies that adds up to over 16p by the end of the year.

Now if I know the monthly rate and I want the yearly rate I would raise the monthly rate to the power 12.

On my spreadsheet that is = 1.01313^12.

If I want to work the other way and get the monthly rate from the yearly one I want the twelth root

= 1.169^(1/12)

That isn't quite 1.01313 because of rounding.

If you make a mistake and leave out the brackets
= 1.169^1/12 a calculator will do 1.169^1 = 1.169 and then divide by 12. wrong answer!

Try some calculations for yourself and then come back to me if you still have questions.

Bob

ps. I used Barclays as an example but the other credit companies do the same thing. See if you can find a different set of rates and try converting the monthly to yearly rates yourself.

Last edited by Bob (2011-03-28 23:54:56)

James893 · 2011-04-25 06:33:56

Hi Ad

I'd save yourself the hassel and just use this compound interest calculator http://www.inspiredtosave.com . It will give you a spreadsheet and graph to refer to showing how your savings increase with time.

I hope this helps.

James

Bob · 2011-04-25 07:33:27

Hi James893,

Thanks for the link. There are a lot of these about and you have to be careful with the way the monthly rates are calculated. In the UK there are differences from the way US interests are quoted.

See http://www.mathisfunforum.com/viewtopic.php?id=15354 for more on this.

Using your link I got 1345 and that isn't what we got by using a spreadsheet and doing one month at a time.

Bob

Math Is Fun Forum

#26 2011-03-17 07:46:45

Re: Compound Interest calculation on savings...

#27 2011-03-28 19:49:36

Re: Compound Interest calculation on savings...

#28 2011-03-28 22:42:38

Re: Compound Interest calculation on savings...

#29 2011-04-25 06:33:56

Re: Compound Interest calculation on savings...

#30 2011-04-25 07:33:27

Re: Compound Interest calculation on savings...

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