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Payment from PV

Calculates the beginning-of-period payment to pay off a present value.

When to use: Use to find lease payments or beginning-of-period withdrawals.

Calculator

Formula

PMT=PV×k1(1+k)n×11+kPMT = PV \times \frac{k}{1 - (1 + k)^{-n}} \times \frac{1}{1 + k}

Variables

SymbolNameDescriptionUnit
PMTPaymentPeriodic payment amount (paid at start of period)$
PVPresent ValueCurrent lump sum value$
kInterest RateNominal annual interest rate%
nNumber of YearsTime period in yearsyears

Real-Life Examples

Example 1: Annual Lease Payment

Equipment worth $50,000, lease at 8% for 5 years, payments at start of year.

Given

PV = 50,000k = 0.08n = 5

Step-by-Step

1.PMT = $50,000 × 0.08 / [1 - (1.08)^(-5)] × 1/(1.08)
2.PMT = $50,000 × 0.2505 × 0.9259
3.PMT = $50,000 × 0.2319
4.PMT = $11,596.85
Result:11,595.21

Beginning-of-year lease payments are $11,596.85.

Example 2: Retirement Withdrawals

$300,000 nest egg, withdraw at start of each year for 20 years, 5% rate.

Given

PV = 300,000k = 0.05n = 20

Step-by-Step

1.PMT = $300,000 × 0.05 / [1 - (1.05)^(-20)] × 1/(1.05)
2.PMT = $300,000 × 0.08024 × 0.9524
3.PMT = $300,000 × 0.07642
4.PMT = $22,926.64
Result:22,926.64

You can withdraw $22,926.64 at the start of each year.

Frequently Asked Questions

Enter the asset value or lease amount as PV, the annual rate as k, and the lease term as n. The formula gives the annual payment due at the start of each year that will fully amortize the lease.

Because each payment is made one period earlier, it earns interest for one extra period. This extra earning power means smaller payments are needed to achieve the same financial result.

Yes. Enter your retirement savings as PV, expected return as k, and years of retirement as n. The result is the maximum beginning-of-year withdrawal that depletes the fund by the end of the term.