Hi Becky ,
Since you want the entire procedure explained , let us start with the basics.
In Simple interest calculations , there are 4 numbers involved viz. Principal (
P) , Interest Rate (
R) , Interest Period (
N) and Interest Amount (
I). The Interest Rate is in percentages , while the Interest Period is in months if the Interest Rate is the rate per month , and in years if the Interest Rate is the annual rate i.e. the rate per year.
Out of these 4 numbers , if any 3 are known , the 4th can be calculated.
It is only if less than 3 are known that we need to resort to What If analysis.
Thus , if we know P , N and R , I is calculated using the mathematical equation I = P * N * R / 100 , where the Interest Rate (
R) is not a percentage number as Excel knows it ( in Excel , when you enter a value such as 10% , what is actually put in the cell or the formula is 0.10 i.e. 10/100 ) , but the number itself. To work out an example , if we invest 15000 ( in any currency ) , at a monthly rate of 6 % , after 24 months , the accumulated interest would be : 15000 * 6 * 24 /100 = 21,600.
As mentioned earlier , if now , we know the values of I , N and R , we can back-calculate P , using the mathematical equation P = 100 * I / ( N * R ). As an example , if we have earned an interest of 6000 , after investing an unknown amount at an annual rate of 8 % , for 5 years , then the principal amount i.e. the amount I would have had to invest , would have been P = 100 * 6000 / ( 8 * 5 ) = 15000.
Now , to your last twist in the tale viz.
50% of the Loan amount will be refunded to the borrower. The 1% interest for 21 months will be a part of the other 50%.
If I have understood this , you mean to say that the interest amount is only on half the principal amount ; we can put it differently , that the actual interest is twice the amount actually mentioned , or for the same interest amount , the principal would be twice the calculated figure. Correct me if I am wrong.
Going by this , P = 2 * 100 * I / ( N * R ). Given your values of I = 640000 , N = 1% monthly , R = 21 months , P would come out to be 2 * 100 * 640000 / ( 1 * 21 ) = 6,095,238.
If you wish to verify these calculations , since the interest is 640000 over 21 months , the monthly interest amount is 640000/21 = 30476.19
Since this is 1 % of the principal , the principal is 100 times this amount i.e. 3,047,619 ; since you say that 50 % of the principal is earning interest ( after 50 % has been given back ) , the actual principal is twice this amount i.e. 2 * 3047619 = 6,095,238.
Narayan