This article describes the Flat Interest Rate amortization method and gives examples of how to calculate payment schedules.

General

The Flat Interest Rate amortization method's prominent feature is that the installment payments are fixed. This method has both fixed monthly* Principal and fixed monthly Interest. Naturally, the Total monthly amount is fixed too (this is what is similar between the Flat Interest Rate and the Annuity (ENG)).

* Monthly installments are the most common, but other installment periods are also possible.

Examples: annually, semi-yearly, quarterly, semi-monthly, bi-weekly, weekly, etc.

How to calculate fixed monthly payment

Fixed monthly payment is calculated according to the formula:

(1)

where

A is the loan amount,

NP is the number of payments;

IR is the monthly interest rate.

Example 1

In this example, the loan Amount is 1000 USD (A = 1,000), the monthly Interest Rate is 1% (IR = 0.01), and the Number of Payments is 3 (NP = 3).

The total amount of fixed monthly payment is calculated according to Formula 1:

The payment schedule looks as follows:

Installment Number	Principal	Interest	Total
1	333.33	10	343.33
2	333.33	10	343.33
3	333.34	10	343.34
Total	1000	30	1030

Example 2

In this example, the Loan Amount is 10,000 USD (A = 10,000), the yearly Interest Rate is 36%, which corresponds to a monthly Interest Rate of 3% (IR = 0.03), and the Number of Payments is 12 (NP = 12).

Parameter	Designation	Value
Loan Amount	A	$10,000.00
Number of Payments	NP	12
Monthly Interest Rate	I	3.00%

The total amount of fixed monthly payment is calculated according to Formula 1:

The payment schedule looks as follows:

Month	Flat Interest	Principal	Total	Outst. Principal	Outst. Balance
				$10,000.00	$13,600.00
1	$300.00	$833.33	$1,133.33	$9,166.67	$12,466.67
2	$300.00	$833.33	$1,133.33	$8,333.34	$11,333.34
3	$300.00	$833.33	$1,133.33	$7,500.01	$10,200.01
4	$300.00	$833.33	$1,133.33	$6,666.68	$9,066.68
5	$300.00	$833.33	$1,133.33	$5,833.35	$7,933.35
6	$300.00	$833.33	$1,133.33	$5,000.02	$6,800.02
7	$300.00	$833.33	$1,133.33	$4,166.69	$5,666.69
8	$300.00	$833.33	$1,133.33	$3,333.36	$4,533.36
9	$300.00	$833.33	$1,133.33	$2,500.03	$3,400.03
10	$300.00	$833.33	$1,133.33	$1,666.70	$2,266.70
11	$300.00	$833.33	$1,133.33	$833.37	$1,133.37
12	$300.00	$833.37	$1,133.37	$0.00	$0.00
Total	$3,600.00	$10,000.00	$13,600.00

Rounding

When dividing the loan amount by the number of installments (Formula 1), a repeating decimal may occur. This leads to a loss of precision. For instance, in Example 2:

This lost precision adds up with every installment and, eventually, effects the total Principal.

Month	Principal (machine precision)	Principal (financial data type precision)	Lost precision	Total precision lost
1	833.33333333	833.33000000	0.00333333	0.00333333
2	833.33333333	833.33000000	0.00333333	0.00666667
3	833.33333333	833.33000000	0.00333333	0.01000000
4	833.33333333	833.33000000	0.00333333	0.01333333
5	833.33333333	833.33000000	0.00333333	0.01666667
6	833.33333333	833.33000000	0.00333333	0.02000000
7	833.33333333	833.33000000	0.00333333	0.02333333
8	833.33333333	833.33000000	0.00333333	0.02666667
9	833.33333333	833.33000000	0.00333333	0.03000000
10	833.33333333	833.33000000	0.00333333	0.03333333
11	833.33333333	833.33000000	0.00333333	0.03666667
12	833.33333333	833.33000000	0.00333333	0.04000000
Total	10000.00000000	9999.96000000	0.04000000	-

To make Total Principal consistent with the Loan Amount, the principal for the last installment is adjusted:

,

where

P_NP is the last scheduled principal amount,

A is the loan amount,

P_i is the amount of principal to be repaid in the i-th month (financial precision).

For instance, in Example 2 the principal for the 12-th installment is calculated as follows: