Rule of 72, Flash Feeling Compounding/Discounting Rate

Rule of 72 is used to have a flash idea of how it can double or halve your present value, PV in compounding or discounting manner respectively. It links the relation between rate and year of holding with the 72, in discounting and compounding manner.

Formula:
n=72/rate

n=holding year in compounding and discounting
rate=annual rate

Example 1: Make it simple to be understood, how long your bank fixed deposits needed to double its value if bank offer 3%p.a?

Based on rule of 72, it requires 24 years.
Working: 72/3 =24.

Actual period is 23.45 years.
Working: in Excel, NPER(0.03,0,-1,2,0)).

Example 2: if the current inflation rate is 6%, how long my favorite coffee price will increase to double from current price?

Based on rule of 72, it requires 12 years from now.
Working: 72/6 = 12.

Actual period is 11.89 years.
Working: in Excel, NPER(0.06,0,-1,2,0))

The basic theory behind the magic 72 is natural logarithm of 2. To get a relationship of double your PV for your FV, let us see the derivation.

FV=PV(1+r)^t, where FV, PV, r and t denote future value, present value, rate and period in year.

2=1*(1+r)^t;
ln(2)=t*ln(1+r), with ln(1+r) approximates to r
thus, 0.693147=t/r (approximation)

Due to 72 is a special number, that has high number of factor of 72 (2, 3, 4, 6, 8, 9, 12, 18, 24 and 36) compared to 69 (3,23) and 71, thus number 72 is chosen to be the flash calculation to capture the idea of how the rate feel like.

How do we use it in daily life?
Example 3: Malaysia credit card charge is 18% p.a, while Singapore is 24% p.a. Does the different of 6% p.a. make a big different?
Let us compare it with rule of 72.

Malaysia rate requires 4 years to double your outstanding balance.
Working: 72/18 = 4.

Singapore rate only requires 3 years to double your outstanding balance.
Working: 72/24 = 3.

Finally, benchmark those rates with local FD rate 2.5%p.a. It requires 28.8 years to get your FD double.
Working: 72/2.5 = 28.8.

So, which one better, to be a lender or borrower? My advice is….be the banker not to be the slave of bank especially credit card.

Diverted original posting from my facebook note dated 22-Oct-09.

Comment:
To understand more, please read the Time Value of Money basic.