Payment from PV
Periodic beginning-of-period payment from a present value with periodic compounding.
When to use: Use for monthly lease payments due at the beginning of each month.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PMT | Payment | Periodic payment amount (paid at start of period) | $ |
| PV | Present Value | Current lump sum value | $ |
| k | Interest Rate | Nominal annual interest rate | % |
| n | Number of Years | Time period in years | years |
| m | Compounding Frequency | Compounding periods per year | integer |
Real-Life Examples
Example 1: Monthly Lease
Lease a $30,000 vehicle at 6% monthly compounding for 4 years, payments at start.
Given
Step-by-Step
Monthly beginning-of-period lease payments are $701.19.
Example 2: Equipment Financing
$15,000 equipment, 7% monthly compounding, 3 years, payments at start of month.
Given
Step-by-Step
Monthly payments at start of month are $460.54.
Frequently Asked Questions
Enter the financed amount as PV, annual rate as k, years as n, and 12 for m. The formula gives the monthly payment due at the beginning of each month that fully covers the obligation over the term.
Yes. Most car leases require payments at the beginning of each month, making them annuities due. Using the annuity due formula ensures accurate payment calculation, compared to the ordinary annuity formula which assumes end-of-month payments.
Annuity due payments are lower by a factor of 1/(1 + k/m). For example, with a 6% annual rate and monthly payments, each annuity due payment is about 0.5% less than the equivalent ordinary annuity payment.