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July 19th, 2019, 08:50 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 458 Thanks: 1  Explain this shortcut C.I solution.
A sum of money placed at Compound interest becomes 27 times of itself in 15 years. In 25 years, it will becomes how many times? Shortcut Sol: 3^3 = 3*5 ?=5*5 ? = 3^5 = 243 times. Actual CI formulae is $\displaystyle CI = P(1+\large\frac{r}{100})\normalsize^{n}$ But solution looks totally different. Please explain. Last edited by skipjack; July 19th, 2019 at 08:55 AM. 
July 19th, 2019, 09:15 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,916 Thanks: 2199 
The sum becomes 3³ times itself in 3*5 years. Hence in 5*5 years, it becomes 3$^{\large3(5*5)/(3*5)}$ times itself, i.e. 3$^{\large5}$ times itself. Alternatively, one can see that the sum becomes 3 times itself in 5 years, so it becomes 3$^{\large n}$ times itself in $5n$ years. For $n$ = 5, this becomes 243 times itself. 
July 19th, 2019, 09:22 AM  #3 
Senior Member Joined: Aug 2014 From: India Posts: 458 Thanks: 1  the sum becomes 3³ times itself means C.I is $\displaystyle 3^3$ bigger than Principal in 15 years? I didn't understand clearly. Last edited by skipjack; July 21st, 2019 at 01:43 AM. 
July 19th, 2019, 10:36 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,916 Thanks: 2199 
It seems easy to understand "A sum of money placed at Compound interest becomes 27 times of itself in 15 years." However, "3^3 = 3*5" in the shortcut solution could mislead if interpreted too literally.

July 20th, 2019, 08:57 AM  #5 
Senior Member Joined: Aug 2014 From: India Posts: 458 Thanks: 1 
Is my interpretation is wrong or right: the sum becomes 3³ times itself means C.I is 3^3 bigger than Principal in 15 years?
Last edited by skipjack; July 21st, 2019 at 01:43 AM. 
July 20th, 2019, 01:34 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,916 Thanks: 2199 
Wrong  it means that the total of the original amount and all the interest earned (including interest on interest) over the 15 years is 3³ times the original amount.

July 20th, 2019, 08:11 PM  #7 
Senior Member Joined: Aug 2014 From: India Posts: 458 Thanks: 1 
It means that the total of the original amount and all the interest earned (including interest on interest) = C.I?
Last edited by skipjack; July 21st, 2019 at 01:44 AM. 
July 20th, 2019, 08:15 PM  #8 
Senior Member Joined: Aug 2014 From: India Posts: 458 Thanks: 1 
Is there any single word for "total of the original amount and all the interest earned" ?

July 21st, 2019, 01:46 AM  #9 
Global Moderator Joined: Dec 2006 Posts: 20,916 Thanks: 2199 
Amount. Your first post used the wording "sum of money", possibly so that you could use that phrase instead of "initial amount" to refer to or define the principal, thus leaving the word "amount" available for the total that you asked about. Sometimes, the principal is defined as a function of time and denoted by, say, P(t), so that P(0) is the initial sum and P(t) is the total amount (including all interest) after time t. This can be done for simple interest just as easily as for compound interest. I've occasionally seen "C.I." used instead of P(t), but I don't recommend doing that. 
July 21st, 2019, 05:22 AM  #10 
Senior Member Joined: Aug 2014 From: India Posts: 458 Thanks: 1 
You mean total amount i.e A = CI + P?


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