I have this question and the answer: Question is how many years and months will
ID: 3142733 • Letter: I
Question
I have this question and the answer:
Question is how many years and months will it take $2million to grow to $5million with an annual interest rate of 7 percent ?
the answer is 13.54 = 13 years , 6.5 months.
I need help understanding how .54 = 6.5 months ...another example is 15.21 thats 15 years but what is the logic to turn the decimal number into months?
http://www.chegg.com/homework-help/m-finance-3rd-edition-chapter-4-problem-31p-solution-9781259322020?trackid=30292a50&strackid=0c83038d&ii=2
Explanation / Answer
The logic here for getting the months is : Simply multiply the given decimal with 12 . This is because 1 year = 12 months . Whenever you have examples like this , go in hierarchial order i.e
years--->months( X 12 ) --->days ( X 30) -->hours (X 24)--->minutes ( X 60 ) --->seconds ( X 60 ).
Every stage present in this order , you have to compare with its previous stage . That is the reason
when you have to find months you multiply by 12 ( 1 year = 12 months )
when you have to find days you multiply by 30 ( 1 month = 30 days )
when you have to find hours you multiply by 24 ( 1 day = 24 hours ) .................and so on
Now , you are given the answer as 13.54 = 13 years ( 0.54 ) months
Multiply 0.54 with 12 = 0.54 *12 = 6.48 or 6.5 months (round of )
If you want to further extend it as part of hierarchial order , it will be =13 years 6 months (0.5 *30 ) days
= 13 years 6 months 15 days
Similarly , the second example that you gave is 15.21 = 15 years ( 0.21 * 12 ) months = 15 years 2.5 months
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And for obvious reasons you cannot change the order , say after years you cannot write days , ex : 13 years 6.5 days which would be wrong . You have to follow the order .
(Please rate if you have understood the logic )