Impress by doing compound interest in your head

I was doing a quick interview for a Tonight with Trevor last week (sometimes I present, sometimes I’m the in-house expert) presented by the very cool Johnny Maitland. Part of the issue was about SAMs (shared appreciation mortgages) a complex mortgage product which has left many in misery. The producers were unsure they’d calculated the APRs right so I did a quick calculation in my head, taking about 20 seconds, which was similar to what they’d worked out; so we were all happy.

Doing this is always greeted by a gobsmacked reaction, after all many people are so scared of numbers the thought of mentally calculating compound interest seems astounding. So of course, I milked it, but now let me tell the truth: it’s all about a simple trick called ‘the rule of 72’, which is elsewhere on the site, but let me explain it in this context. You need to understand how interest works first, if not read my (cunningly named) how interest works article.

How the rule of 72 works

Divide 72 by the interest rate to see how long it takes to double. For example at 12% interest save £1,000 and you’d have £2,000 (ie. double) in (72 divided by 12 equals 6) six years. At 5% interest save £1,000 and it would take (72 divided by 5 equals 14.4) around fourteen and a half years. This holds pretty true for all percentages under 20%. –

So on to the sum I worked out:

I’ve forgotten the exact amounts, but it was something like “what is the APR, ie annual interest rate, if you borrowed £80,000 and had to repay 200,000 six years later?” As part of SAMS, no repayment is made in the meantime (or its a different type of sum, still do-able though, see my past ‘calculating personal loan interest in your head‘ blog) so its just a simple piece of compound interest.

This was the logic process I followed…

A. 200,000 is 2.5 times 80,000 – so in six years the amount owed has increased by 2.5 times.

B. As it takses six years to increase 2.5 times, it doubles roughly every 4.5 years. This is a crucial estimate, and its important to remember than the growth isn’t linear (in other words, doubling means the amount the debt increases every year grows. E.g it doubles once and you’ve 2 times the original amount (ie 1 more) , it doubles again and you’ve four times (ie 2 more in that period), it doubles again and you’ve 8 times (ie its increased by 4….. and so on – so when you estimate you need to factor this in).

C. Then using the rule of 72, simply divide 72 by 4.5 which is 16.

Therefore the APR rate is around 16%. Right now let me go check that in a calculator….. and the actual answer is 16.4% – close enough!

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