How Do I Calculate The Monthly Payment Schedule Indicating Both Principle Payment And Interest Pymt?
Beginning Nov. 1 2006, I loaned a friend $2200/month. The interest rate was 10% per year effective Nov 1, 2006. The same amt provided (last principle pymt) each month thru Dec. 31, 2008. My friend will start paying back the loan beginning Jan 1, 2009 for 48 months.
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If you compound the interest monthly, the value of the string of payments to your friend is
FV = A(1+r)((1+r)n-1)/r
where A is the payment amount, r is the interest rate per period (month), and n is the number of periods (months). This will compute the value at the end of the month in which the final payment was made.
FV = 2200(1+.10/12)((1+.10/12)26-1)/(.10/12)
FV = 2200*29.138683 = 64,105.10
_____
If you charge 10% interest on the outstanding balance each month during the payback period, the payment will be
A = Pr/(1-(1+r)-n)
where A is the payment, P is the principal amount, r is the monthly interest rate, and n is the number of months.
A = P((.10/12)/(1 - (1+.10/12)-48) = P*.0253626
For a principal amount of $64,105.10, the loan payment amount will be $1625.87 per month.
_____
These numbers assume you carry enough digits in the calculations so that the results are not affected by the precision of the math. If you round the interest charged to the nearest penny each month, the total loan amount (for compound interest) comes to $64,105.11 according to my spreadsheet.
My spreadsheet is in the attached picture. (If you use $1625.87 as the payback amount, the balance is $.07 at the end of 4 years. If you use $1625.88, the balance is -$.55, so the final payment can be smaller by that amount.)
FV = A(1+r)((1+r)n-1)/r
where A is the payment amount, r is the interest rate per period (month), and n is the number of periods (months). This will compute the value at the end of the month in which the final payment was made.
FV = 2200(1+.10/12)((1+.10/12)26-1)/(.10/12)
FV = 2200*29.138683 = 64,105.10
_____
If you charge 10% interest on the outstanding balance each month during the payback period, the payment will be
A = Pr/(1-(1+r)-n)
where A is the payment, P is the principal amount, r is the monthly interest rate, and n is the number of months.
A = P((.10/12)/(1 - (1+.10/12)-48) = P*.0253626
For a principal amount of $64,105.10, the loan payment amount will be $1625.87 per month.
_____
These numbers assume you carry enough digits in the calculations so that the results are not affected by the precision of the math. If you round the interest charged to the nearest penny each month, the total loan amount (for compound interest) comes to $64,105.11 according to my spreadsheet.
My spreadsheet is in the attached picture. (If you use $1625.87 as the payback amount, the balance is $.07 at the end of 4 years. If you use $1625.88, the balance is -$.55, so the final payment can be smaller by that amount.)
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