Does the formula P(1+r)n mean anything to you? Unless you are a mathematician,
the answer is probably no, and yet of all mathematical equations, it is
arguably the most important to our daily lives because banks use it to
determine how much we should receive on our savings and how much we owe on
our debts.
It is the formula for basic compound interest, where P stands for principle,
or the amount of capital, r is the interest rate and n is the number of
years. Mercifully, most of us never have to use it because the banks do the
calculation for us.
However, experts say that a grasp of more basic mathematics is key to managing
money, and if taught as part of personal finance in schools, it could help
to erode the UK's £1.4 trillion debt mountain.
Supporters of personal finance education are lobbying to change the curriculum
so that money matters are taught as a single subject, using basic maths to
solve real-life financial problems. Anne Kiem, a former maths teacher and
director at the ifs School of Finance, the financial education group, says:
“The mismanagement of money is a key cause of many of the social problems
facing society today. Levels of personal bankruptcy and personal debt are
soaring. Almost all of this mismanagement is a result of financial
ignorance.”
While changes to the curriculum will come too late for anyone not of school
age, it is not too late to learn the basics.
Mortgages
While it is possible to work out how much your mortgage will cost by yourself,
it is labour-intensive and unnecessary, as most big brokers, such as London &
Country (www.lcplc.co.uk), have mortgage calculators on their websites.
These work out how much it will cost a month, how much you can borrow and
what the repayments would be for different interest rates and loan amounts.
However, there are a couple of snags. First, some lenders, including Bristol &
West and a number of small building societies, calculate interest monthly or
annually, rather than daily. Borrowers paying interest monthly or yearly
will end up paying more because the capital is eroded more slowly, but it is
often difficult to verify how much more because most calculators on the
internet assume daily calculations. Ray Boulger, of John Charcol, the
mortgage broker, says: “Be careful not to get caught out by lenders that do
not apply interest daily. This makes a significant difference over the term
of the loan.”
The other important thing to consider when repaying both the capital and the
interest on a mortgage is that, at the beginning of the repayment term,
virtually all of your money is going on the interest. Repayments do not
begin to eat into the capital that you have borrowed until much later. “This
means that the lower the interest rate, the more quickly you will begin to
pay off some of the capital,” Mr Boulger says.
For instance, on a £150,000 loan with a rate of 5.5 per cent, the interest
repaid in the first year would be £8,178, compared with £2,875 of capital.
If the rate were 7.34 per cent, interest paid would be £10,937, compared
with £2,177 of capital.
Pensions and savings
With interest on savings, the important thing to remember is that the more
regular the investment, the more interest you will accumulate. Likewise, the
earlier you begin saving in a pension, the more interest you will receive at
retirement. This is because compound interest is basically interest on top
of interest already earned. So 5 per cent interest on a savings pot of £100
in Year 1 will give an investment of £105 after a year. In Year 2, the saver
will earn 5 per cent on £105, which is £5.25 -a bigger return.
This means that someone investing £1,000 a year for ten years between the ages
of 20 and 30 will receive far more in interest when he or she reaches 40
than someone who invests the same amount between the ages of 30 and 40. The
first saver will have saved £21,512, while the second will have earned
£14,207.
To play around with different amounts and rates, use the calculator at
www.moneymatterstome.co.uk/interactivetools. However, remember to deduct tax
from interest earned on savings, according to whether you are a higher or
lower-rate taxpayer.
While working out the interest you will earn on savings is relatively
straightforward, pension estimates are much more difficult because they
usually involve a mixture of investments including shares and bonds. Workers
in money purchase schemes should try the estimator produced by the
Association of British Insurers at www.pensioncalculator.org.uk.
Credit cards and loans
Card and loan companies charge an APR, or annual percentage rate. Best-buy
loans are available for about 7 per cent, while credit cards usually charge
about 15 per cent after the expiry of any offer period. However, the amount
of interest that you will actually pay is complicated by how much you repay
and how often. For instance, if you were to take a £10,000 loan at 7 per
cent and pay it back over 12 months, the monthly repayments would be £865
and the total interest would be £383. However, if you borrowed £10,000 at 7
per cent over five years, the monthly repayments would be lower at £198, but
the total interest would be £1,880.
For a more accurate picture of how much interest you will pay, it is useful to
calculate the monthly rate. To do this, divide the APR by 12 for a rough
estimate. On a 7 per cent loan, this is 0.565 per cent.
The accumulation of interest is the main reason why credit card borrowers
should pay more than the minimum monthly repayment.
Card companies also apply a negative payment hierarchy, which means that
repayments go towards the part of your debt with the lowest interest rate
first. The most expensive debt is not reduced until the cheaper debt has
been cleared. Nationwide Building Society is among only a handful of card
issuers that do not do this.
The Financial Services Authority has useful interest and repayment calculators
at www.moneymadeclear.fsa.gov.uk. For tax calculators, the best website is
www.digita.com.
CASE STUDY: Mortgage school
Mohammed Sayid, says that he had no real understanding of money matters until
he began a programme in personal financial planning for adults, run by the
ifs School of Finance.
The 20-year old, from East London, applied after seeing the course advertised
in a local newspaper. “The only knowledge I had came from family, friends,
bank staff and advertisements, which wasn't much,” he says.
“You need basic maths to apply some of the concepts - for instance, to work
out what a 10 per cent deposit would be on a £200,000 house - but there is
no link with pure maths. The course is more about concepts and theories,
such as the pros and cons of different types of mortgage.”
Test yourself
1. If you took a loan for £10,000 over five years at an interest rate
of 7 per cent, how much would the monthly repayments be?
2. What is the difference between the interest you would recieve if you
saved £50 a month for two years in an account paying 5 per cent, compared
with £100 a month over the same period?
3. On a £150,000 mortgage at 5.5 per cent over 25 years (interest
calculated monthly), what is the total amount repayable?
4. Which loan would cost more in interest: (a) £10,000 over five years
at 5 per cent; (b) £10,000 over three years at 8 per cent?
5. Which returns more after two years (interest calculated annually):
(a) an account with a rate of 7 per cent in the first year and 5 per cent in
the second; (b) an account with a fixed rate of 6 per cent.
Answers: 1. £198, 2. £60, 3. £276,339, 4. (a), 5. (b) by 10p
It's psychology, rather than math, which is will helps most in managing money matters.
It's really funny for a Ukrainian to see the discussed the difference between UK mortgage payments of 5.5 and 7.34.
In Ukraine, you would have a mortgage with a 12,25% (or more) interest rate, and fines for early payments. It's actually depressing to calculate what the payments for a 25-year mortgage on such terms will be.
Yet this not stop people (economists being among them) from applying for such mortgages. If the social pressure is to have a decent apartment now, the excessive payments on a mortgage tend to play a smaller role in deciding whether to apply for a loan...
Mykyta , Kyiv, Ukraine
I should have made it clear I calculated using 'Flate Rate' interest. This is how most car dealers will work out a finance document. It will then be expressed as an 'APR' to keep legal etc. Not wrong then, just different. Had Q1 stated 7% APR then it would have been clear you pay £198 and not £225 as you would pay for your car loan. Be vigilant is a lesson to learn in all matters financial.
len turner, maidstone, UK
Looking at the responses to this article there are a few interesting points that have been raised.
The formula right at the start is printed incorrectly. The "n" on the end is an exponent. It should be like something like this: P(1+r)^n.
Eniyan has shown us the way forward with the handling of question 1, Test yourself. Thankyou.
Compare this to Len's attempt at the same problem. This highlights what I said in the 3rd paragraph to 'my say.' The principles involved are simple enough to apply, but only when you know how to work the numbers.
Judging by the other responses so far, the importance of making the distinction seems to be in dispute.
But consider this. Surely we owe it to ourselves to know something of our own affairs at ground level, especially when it comes to finance in dumbed-down Britain. If the banks can't even get important matters right these days how can anyone feel safe leaving them to fiddle the numbers (while the global economy burns).
Mark, Hastings, East Sussex
£225 is wrong. You have not taken into account that the loan decreases year on year and therefore the interest is less.
£198 has balanced out this decreasing interest and set a standard payment for the 5 years.
barbara, north east,
Question 2 - How do you spell 'receive'?
Chris, Worcester,
£198 is correct.
Use
R = 0.07/12 (monthly interest rate)
N = 12x5 (number of months)
P = 10000 (principal)
monthly repayment, M is
M = P x R x (1 + R)^N
----------------------
(1 + R)^N - 1
Eniyan, Bristol,
This article gives people an excuse to not calculate anything and as they just say the maths is to difficult.
I am a mathematician and I have NEVER calculated any interest payments myself. The banks do that for you (together with total amount to pay!)
You don't need any maths, just compare the APR/AER - that's it. It is as easy as comparing 5 with 6 and realising that 6 is the bigger number.
Stefan, Newbury,
If you pay off ANY of the capital in year 1 then you no longer need to pay 7% interest on that part of the debt. Equal monthly payments will cover interest on entire loan at first, but this will only be a small component of the final payments.
Nigel H, Ipswich, UK
Test Yourself 1. above?
£10000 loan for 5 years at 7%? = £10000 x 7% = £700 x 5 years = £3500 + £10000 = £13500 divide this by the 60 months (5years) = £225 per month.
How do you arrive at £198? answers please.
len turner, maidstone, UK
Anyone agree with above answer to No.1 I make this £225 not £198.
len turner, maidstone, UK
Everyone in 21st century Britain should know how to calculate their mortgage package as a prerequisite to obtaining their mortgage.
Many maths books available from off the shelf dealing with standard GCSE subject matter do, I am pleased to say, provide the necessary formulae and general algebra for doing so. There's nothing to stop even the marginally inquisitive from going out to buy this type of book. The real problem is probably not just that of learning the method, but of applying the abstractions therein to real life.
Knowing how to crunch the numbers seems to be an increasingly relevant skill in a age when the cost of living is sky-rocketing and pockets are shrinking in size. For instance, the non-linear aspects associated with credit terms need to be understood by anyone considering the undertaking of borrowing in order to project a domestic budget . Far better to put it all down on paper, or into a speadsheet before proceeding, than for it all to end in tears.
Mark, Hastings, East Sussex