Shortcut #2 to compute interest:

————-

(i) When interest is calculated as CI, the number of years for the Amount to double (two times the principal) can be found with this following formula:

P * N ~ 72 (approximately equal to).

Exampe, if R=6% p.a. then it takes roughly 12 years for the Principal to double itself.

Note: This is just a approximate formula (when R takes large values, the error % in formula increases).

(ii) When interest is calculated as SI, number of years for amt to double can be found as:

N * R = 100 . BTW this formula is exact!

Adding to what ‘Peebs’ said, this shortcut does work for any P/N/R.

Basically if you look closely at this method, what I had posted is actually derived from the Binomial expansion of the polynomial — (1+r/100)^n but in a more “edible” format digestable by us!

BTW herez one shortcut on recurring decimals to fractions …Its more easier to explain with an example..

Eg: 2.384384384 ….

Step 1: since the 3 digits ’384′ is recurring part, multiply 2.384 by 1000 = so we get 2384.

Next ’2′ is the non recurring part in the recurring decimal so subtract 2 from 2384 = 2382.

If it had been 2.3848484.., we would have had 2384 – 23 = 2361. Had it been 2.384444.. NR would be 2384 – 238 = 2146 and so on.

We now find denominator part …….

Step 3: In step 1 we multiplied 2.384384… by 1000 to get 2384, so put that first.

Step 4: next since all digits of the decimal part of recurring decimal is recurring, subtract 1 from step 3. Had the recurring decimal been 2.3848484, we need to subtract 10. If it had been 2.3844444, we needed to have subtracted 100 ..and so on…

Hence here, DR = 1000 – 1 = 999

Hence fraction of the Recurring decimal is 2382/999!!

Some more examples ….

1.56787878 … = (15678 – 156) / (10000 – 100) = 15522/9900

23.67898989… = (236789 – 2367) / (10000 – 100) = 234422/9900

124.454545… = (12445 – 124) / (100 – 1) = 12321/99