Solver Personal Finance: Convert simple interest to equivalent compound interest for a given period

Source code of 'Personal Finance: Convert simple interest to equivalent compound interest for a given period'

This Solver (Personal Finance: Convert simple interest to equivalent compound interest for a given period) was created by by Shruti_Mishra(0)

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About Shruti_Mishra: I am a maths graduate from India and am currently persuing masters in Operations Research.

==section input
Find Compound Interest (annual compounding), given Principal = $ *[input p=1000], Simple Interest = *[input si=100]% and Time = *[input t=2] years. The interest rate is same for both simple and compound interest.

==section solution

We need to first calculate the <A HREF="interest_rate.lesson">interest rate</A> for the given simple interest. This can be calculated as follows:
 
The formula for finding <A HREF="interest_rate.lesson">Interest Rate</A> for <A HREF="simple_interest.lesson">Simple interest</A> is: 
Interest Rate = {{{Simple Interest /(Principal * Time)*100}}}%. 
 
Thus for the given values of P= $p , I = $si and T = $t , the <A HREF="interest_rate.lesson">interest rate</A> would be
R = $si/($p * $t)*100 = *[assign r=$si/($p*$t)*100] $r% per annum.
 
So, the <A HREF="interest_rate.lesson">interest rate</A> is $r% per annum
 
Now we calculate the <A HREF="compound_interest.lesson">compound interest</A> as follows:
The formula for finding <A HREF="compound_interest.lesson">compound interest</A> is: 
Interest = {{{Principal * (1 + Rate)^Time - Principal}}}.
 
Thus for the given values of P= $p , R = $r% and T = $t , the <A HREF="compound_interest.lesson">compound interest</A> would be
I = $p * (1+ $r/100)^$t -$p = *[assign ci=$p*(1 + $r/100)^$t -$p] $ $ci.
 
So, the interest amount is $ci and the total payable amount is $ci + $p = *[assign n=$ci+$p] $n

==section output
ci

==section check
  p=1000 si=100 t=2 ci=102.5