£1,000? Each year he gets £70 interest so all he has to do is divide 1000 by 70.
This gives 14.29 so that he can be sure in 15 years he will have more than
£2000 in the bank. It is a long time to wait. To show the superiority of
compound interest Charlie starts to calculate his own doubling period. This is a
little more complicated but a friend tells him about the rule of 72.
The rule of 72
For a given percentage rate, the rule of 72 is a rule of thumb for estimating
the number of periods required for money to double. Though Charlie is
interested in years the rule of 72 applies to days or month as well. To find the
doubling period all Charlie has to do is to divide 72 by the interest rate. The
calculation is 72/7 = 10.3 so Charlie can report to his brother that his investment
will double in 11 years, much quicker than Simon’s 15. The rule is an
approximation but it is useful where quick decisions have to be made.
Present value Compound Charlie’s father is so impressed by his son’s good
sense that he takes him aside and says ‘I propose to give you £100,000’. Charlie
is very excited. Then his father adds the condition that he will only give him the
£100,000 when he is 45 and that won’t be for another ten years. Charlie is not so
happy.
Charlie wants to spend the money now but obviously he cannot. He goes to
his bank and promises them the £100,000 in ten years time. The bank responds
that time is money and £100,000 in ten years time is not the same as £100,000
now. The bank has to estimate the size of investment now that would realize
£100,000 in ten years. This will be the amount they will loan to Charlie. The
bank believes that a growth rate of 12% would give them a healthy profit. What
would be the amount now that would grow to £100,000 in ten years, at 12%
interest? The compound interest formula can be used for this problem as well.
This time we are given A = £100,000 and have to calculate P, the present value
of A. With n = 10 and i = 0.12, the bank will be prepared to advance Charlie the
amount 100,000/1.12^10 = £32,197.32. Charlie is quite shocked by this small
figure, but he will still be able to buy that new Porsche.