Flat Interest Rate
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
PNP is the last scheduled principal amount,
A is the loan amount,
Pi 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:
