185. The Formula for Compound Interest

When considering investments, consider the power of compounding. Compound interest is where the interest you have earned is added to the investment and it itself generates more interest : The formula is as follows :

A = P(1 + r/q)nq

The nq outside the brackets above does not mean "multiplied by nq" but "to the power of nq".

P is the principal (the money you start with, your first deposit)

r is the annual rate of interest as a decimal (5% means r = 0.05)

n is the number of years you leave it on deposit

A is how much money you've accumulated after n years, including interest.

If the interest is compounded once a year:

A = P(1 + r)n

If the interest is compounded q times a year:

A = P(1 + r/q)nq


As a good exercise you should work out dozens of examples comparing the returns when interest is compounded and when it is just simple interest (SI = PRT/100).

Formula for the present value (discounted value) of a future amount

P = the present value of amount A, due n years from now

r = the rate of interest

For example, someone contracts to pay you $100,000 in ten years. What's that worth right now, if they changed their mind and decided to paid you upfront? Say the interest rate is 5%.

At simple interest:

P = A/(1 + nr)

If A = 100,000 and n = 10 and r = 0.05 (which is to say, 5%), then

P = 100,000/(1 + 10x0.05) = 100,000/1.5 = 66,667

At interest compounded annually:

P = A/(1 + r)n

Using the same example as for simple interest, this gives

P = 100,000/(1 + .05)10 = 100,000/1.62889 = 61,391

At interest compounded q times a year:

P = A/(1 + r/q)nq

Or in the same example but compounding monthly (q = 12)

P = 100,000/(1 + 0.05/12)120 = 100,000/1.64701 = 60716

168. Credit Cards

Beware of Credit Cards. If you owe €2,000 on your card and the interest rate is 19.5% and you only pay the minimum amount, it will take you 41 years to pay it off ! Credit cards are unsecured and the most expensive product a bank will sell you. More expensive still are store cards, their interest rate is 29%, minimum.

Only ever use a credit card as a payment mechanism rather than a method of borrowing. This means that you should use your card when out and about but make sure that you pay it off in full and on time within the month. This eliminates or minimises the interest charge and avoids the late payment fee.

Never pay Payment Protection Insurance on your card. THIS IS A SCAM. PPI raises the effective interest by 7% and it only pays out the minimum payment - NOT THE FULL BALANCE and then only covers you for 1 year. In addition, the charges are added each month to your credit card balance, increasing the principal.

Credit cards are a very dangerous weapon used by the system against you. They are designed to keep you poor. If you must have one be very careful how much you spend on it and do try to have a 0% one. Beware of these too, as the interest-free period expires after 6 or 9 months.

Even better than a credit card, have an American Express or Diners Club catd. These are charge cards and must be cleated in full every month.

A debit card (laser) is even better because it only allows you to access funds that you already have. With these, there is no element of borrowing unless you use it to run up your overdraft.

Generally speaking, credit cards are extremely dangerous brcause they are the fastest way into big, big debt. You should treat them as you would a loaded gun or a fully primed Mills bomb.