Compound interest formula
When talking about mathematics, it is always good to have Albert Einstein on
side – but the widespread claim that he said compound interest is the greatest
discovery of all time is too far-fetched. That the formula for compound interest
has a greater immediacy than his E = mc^2 is undeniable. If you save money,
borrow money, use a credit card, take out a mortgage or buy an annuity, the
compound interest formula is in the background working for (or against) you.
What do the symbols stand for? The term P stands for principal (the money you
save or borrow), i is the percentage interest rate divided by 100 and n is the
number of time periods.
Charlie places his £1000 in an account paying 7% interest annually. How
much will accrue in three years? Here P = 1000, i = 0.07 and n = 3. The symbol
A represents the accrued amount and by the compound interest formula
A=£1225.04.
Simon’s account pays the same interest rate, 7%, as simple interest. How do
his earnings compare after three years? For the first year he would gain £70 in
interest and this would be the same in the second and third years. He would
therefore have 3 × £70 interest giving a total accrued amount of £1210. Charlie’s
investment was the better business decision.
Sums of money that grow by compounding can increase very rapidly. This is
fine if you are saving but not so good if you are borrowing. A key component of
compound interest is the period at which the compounding takes place. Charlie
has heard of a scheme which pays 1% per week, a penny in every pound. How
much would he stand to gain with this scheme?
Simon thinks he knows the answer: he suggests we multiply the interest rate
1% by 52 (the number of weeks in the year) to obtain an annual percentage rate
of 52%. This means an interest of £520 making a total of £1520 in the account.
Charlie reminds him, however, of the magic of compound interest and the
compound interest formula. With P = £1000, i = 0.01 and n = 52, Charlie
calculates the accrual to be £1000 × (1.01)^52. Using his calculator he finds this is
£1677.69, much more than the result of Simple Simon’s sum. Charlie’s
equivalent annual percentage rate is 67.769% and is much greater than Simon’s
calculation of 52%.
Simon is impressed but his money is already in the bank under the simple
interest regime. He wonders how long it will take him to double his original
marcin
(Marcin)
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