Compounding interval functionality
This article provides information to help choose monthly, quarterly, semiannual, and annual compounding intervals. The compounding interval functionality is used to determine the number of compounding periods per year in a lease's payment schedule. Each of the four examples in this article shows what a lease's payment schedule looks like for a different interval.
You can't select a compounding interval that is less frequent than the lease's payment frequency. For example, a quarterly compounding interval can't be used with a monthly payment frequency, and an annual compounding interval can't be used with a semiannual payment frequency. If you try to select a compounding interval that is less frequent than the lease's payment frequency, you receive an error message.
Note
In all four examples in this article, the compounding interval matches the payment frequency.
Examples
Setup for all four leases
The following tables show the values that are set on the General and Payment schedule lines tabs for the four leases that are used in the examples.
General tab
| Field | Value |
|---|---|
| Incremental borrowing rate | 5% |
| Annuity type | Ordinary annuity |
| Compounding interval | See the individual examples. |
| Payment frequency | Monthly |
| Commencement date | 1/1/2020 |
Payment schedule lines tab
| Field | Value |
|---|---|
| Start date | 1/1/2020 |
| Periods | 120 |
| Period interval | Months |
| End date | 12/31/2029 |
| Payment frequency | See the individual examples. |
| Payment amount | 50,000 |
Lease 1: Monthly compounding interval and monthly payment frequency
The following table lists the first 12 months of the payment schedule. Note the following details:
- The value in the "Period" column increases by 1 every month, because each month is a new compounding interval.
- In the formula in the "Present value" column, the rate is divided by 12, because there are 12 compounding periods per year. The exponent (the superscript numeral) equals the value in the "Period" column.
| Period | Month | Date | Payment amount | Present value |
|---|---|---|---|---|
| 1 | 1 | 1/31/2020 | 50,000.00 | 50,000 ÷ (1 + [5% ÷ 12])1 = 49,792.53 |
| 2 | 2 | 2/29/2020 | 50,000.00 | 50,000 ÷ (1 + [5% ÷ 12])2 = 49,585.92 |
| 3 | 3 | 3/31/2020 | 50,000.00 | 50,000 ÷ (1 + [5% ÷ 12])3 = 49,380.17 |
| 4 | 4 | 4/30/2020 | 50,000.00 | 50,000 ÷ (1 + [5% ÷ 12])4 = 49,175.28 |
| 5 | 5 | 5/31/2020 | 50,000.00 | 50,000 ÷ (1 + [5% ÷ 12])5 = 48,971.23 |
| 6 | 6 | 6/30/2020 | 50,000.00 | 50,000 ÷ (1 + [5% ÷ 12])6 = 48,768.03 |
| 7 | 7 | 7/31/2020 | 50,000.00 | 50,000 ÷ (1 + [5% ÷ 12])7 = 48,565.67 |
| 8 | 8 | 8/31/2020 | 50,000.00 | 50,000 ÷ (1 + [5% ÷ 12])8 = 48,364.15 |
| 9 | 9 | 9/30/2020 | 50,000.00 | 50,000 ÷ (1 + [5% ÷ 12])9 = 48,163.47 |
| 10 | 10 | 10/31/2020 | 50,000.00 | 50,000 ÷ (1 + [5% ÷ 12])10 = 47,963.62 |
| 11 | 11 | 11/30/2020 | 50,000.00 | 50,000 ÷ (1 + [5% ÷ 12])11 = 47,764.61 |
| 12 | 12 | 12/31/2020 | 50,000.00 | 50,000 ÷ (1 + [5% ÷ 12])12 = 47,566.41 |
Lease 2: Quarterly compounding interval and quarterly payment frequency
The following table lists the first 12 months of the payment schedule. Note the following details:
- The value in the "Period" column increases by 1 every three months (that is, every quarter), because each quarter is a new compounding interval.
- In the formula in the "Present value" column, the rate is divided by 4, because there are four compounding periods per year. The exponent equals the value in the "Period" column.
| Period | Month | Date | Payment amount | Present value |
|---|---|---|---|---|
| 1 | 1 | 1/31/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 4])1 = 0 |
| 1 | 2 | 2/29/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 4])1 = 0 |
| 1 | 3 | 3/31/2020 | 50,000.00 | 50,000 ÷ (1 + [5% ÷ 4])1 = 49,382.72 |
| 2 | 4 | 4/30/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 4])2 = 0 |
| 2 | 5 | 5/31/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 4])2 = 0 |
| 2 | 6 | 6/30/2020 | 50,000.00 | 50,000 ÷ (1 + [5% ÷ 4])2 = 48,773.05 |
| 3 | 7 | 7/31/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 4])3 = 0 |
| 3 | 8 | 8/31/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 4])3 = 0 |
| 3 | 9 | 9/30/2020 | 50,000.00 | 50,000 ÷ (1 + [5% ÷ 4])3 = 48,170.92 |
| 4 | 10 | 10/31/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 4])4 = 0 |
| 4 | 11 | 11/30/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 4])4 = 0 |
| 4 | 12 | 12/31/2020 | 50,000.00 | 50,000 ÷ (1 + [5% ÷ 4])4 = 47,576.21 |
Note
If the annuity type is changed to Annuity due, the payment will be at the beginning of the quarter instead of the end of the quarter.
Lease 3: Semiannual compounding interval and semiannual payment frequency
The following table lists the first 12 months of the payment schedule. Note the following details:
- The value in the "Period" column increases by 1 every six months (that is, semiannually), because each half-year is a new compounding interval.
- In the formula in the "Present value" column, the rate is divided by 2, because there are two compounding periods per year. The exponent equals the value in the "Period" column.
| Period | Month | Date | Payment amount | Present value |
|---|---|---|---|---|
| 1 | 1 | 1/31/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 2])1 = 0 |
| 1 | 2 | 2/29/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 2])1 = 0 |
| 1 | 3 | 3/31/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 2])1 = 0 |
| 1 | 4 | 4/30/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 2])1 = 0 |
| 1 | 5 | 5/31/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 2])1 = 0 |
| 1 | 6 | 6/30/2020 | 50,000.00 | 50,000 ÷ (1 + [5% ÷ 2])1 = 48,780.49 |
| 2 | 7 | 7/31/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 2])2 = 0 |
| 2 | 8 | 8/31/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 2])2 = 0 |
| 2 | 9 | 9/30/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 2])2 = 0 |
| 2 | 10 | 10/31/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 2])2 = 0 |
| 2 | 11 | 11/30/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 2])2 = 0 |
| 2 | 12 | 12/31/2020 | 50,000.00 | 50,000 ÷ (1 + [5% ÷ 2])2 = 47,590.72 |
Note
If the annuity type is changed to Annuity due, the payment will be in January and July instead of June and December.
Lease 4: Annual compounding interval and annual payment frequency
The following table lists the first 12 months of the payment schedule. Note the following details:
- The value in the "Period" column increases by 1 every 12 months (that is, annually), because each year is a new compounding interval.
- In the formula in the "Present value" column, the rate is divided by 1, because there is one compounding period per year. The exponent equals the value in the "Period" column.
| Period | Month | Date | Payment amount | Present value |
|---|---|---|---|---|
| 1 | 1 | 1/31/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 1])1 = 0 |
| 1 | 2 | 2/29/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 1])1 = 0 |
| 1 | 3 | 3/31/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 1])1 = 0 |
| 1 | 4 | 4/30/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 1])1 = 0 |
| 1 | 5 | 5/31/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 1])1 = 0 |
| 1 | 6 | 6/30/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 1])1 = 0 |
| 1 | 7 | 7/31/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 1])1 = 0 |
| 1 | 8 | 8/31/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 1])1 = 0 |
| 1 | 9 | 9/30/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 1])1 = 0 |
| 1 | 10 | 10/31/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 1])1 = 0 |
| 1 | 11 | 11/30/2020 | 0.00 | 0.00 ÷ (1 + [5% ÷ 1])1 = 0 |
| 1 | 12 | 12/31/2020 | 50,000.00 | 50,000 ÷ (1 + [5% ÷ 1])1 = 47,619.05 |
Note
If the annuity type is changed to Annuity due, the payment will be in January instead of December.