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.