This article describes the Flat Interest Rate lending scheme and gives examples on how to calculate payment schedules.
General
The Flat Interest Rate lending scheme is a fixed payment lending scheme. This scheme has 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 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 principle amount,
A is the loan amount,
Pi is the amount of principal to be repaid in i-th month (financial precision).
For instance, in Example 2 the principal for the 12-th installment is calculated as follows:
