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The denominator of a Rule of 78s loan is the sum of the integers between 1 and n, inclusive, where n is the number of payments. For a twelve-month loan, the sum of numbers from 1 to 12 is 78 (1 + 2 + 3 + . . . +12 = 78). For a 24-month loan, the denominator is 300. The sum of the numbers from 1 to n is given by the equation n * (n+1) / 2.
Using the Rule of 78, a $5,000 personal loan with an interest rate of 11 percent over 48 months and a $150/mo payment would incur an interest charge of $89.80 in the first month.
An early reference to the rule is in the Summa de arithmetica (Venice, 1494. Fol. 181, n. 44) of Luca Pacioli (1445–1514). He presents the rule in a discussion regarding the estimation of the doubling time of an investment, but does not derive or explain the rule, and it is thus assumed that the rule predates Pacioli by some time.
For example, with an annual growth rate of 4.8% the doubling time is 14.78 years, and a doubling time of 10 years corresponds to a growth rate between 7% and 7.5% (actually about 7.18%). When applied to the constant growth in consumption of a resource, the total amount consumed in one doubling period equals the total amount consumed in all ...
Using the Rule of 72, your money should double every 10.3 years. So, by age 45, you should have around $200,000 in retirement savings. By age 55, you should have around $400,000.
The Rule of 72 works best in the range of 5 to 10 percent, but it’s still an approximation. To calculate based on a lower interest rate, like 2 percent, drop the 72 to 71.
MARPOL 73-78 Instructions. MARPOL Annex V (Regulations for the Prevention of Pollution by Garbage from Ships) came into force on 31 December 1988. It specifies the distances from land in which materials may be disposed of and subdivides different types of garbage and marine debris.
The rule of 25 vs. 4% rule. The rule of 25 is just a different way to look at another popular retirement rule, the 4% rule. It flips the equation (100/4% = 25) to emphasize a different part of the ...