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Payment from FV

Calculates the periodic payment needed to reach a future value with m-period compounding.

When to use: Use to find monthly or quarterly savings needed to reach a goal.

Calculator

Formula

PMT=FV×km(1+km)n×m1PMT = FV \times \frac{\frac{k}{m}}{\left(1 + \frac{k}{m}\right)^{n \times m} - 1}

Variables

SymbolNameDescriptionUnit
PMTPaymentPeriodic payment amount$
FVFuture ValueFuture lump sum value$
kInterest RateNominal annual interest rate as a decimal%
nNumber of YearsTime period in yearsyears
mCompounding FrequencyCompounding periods per yearinteger

Real-Life Examples

Example 1: Monthly Savings Goal

You need $100,000 in 10 years. Rate is 6% compounded monthly. How much per month?

Given

FV = 100,000k = 0.06n = 10m = 12

Step-by-Step

1.PMT = $100,000 × (0.005) / [(1.005)^120 - 1]
2.PMT = $100,000 × 0.005 / 0.8197
3.PMT = $100,000 × 0.006102
4.PMT = $610.21
Result:610.21

Save $610.21/month to reach $100,000 in 10 years.

Example 2: Emergency Fund

Build a $20,000 emergency fund in 3 years at 4% monthly compounding.

Given

FV = 20,000k = 0.04n = 3m = 12

Step-by-Step

1.PMT = $20,000 × (0.04/12) / [(1 + 0.04/12)^36 - 1]
2.PMT = $20,000 × 0.01573
3.PMT = $524.34
Result:523.81

Save $524.34/month to build a $20,000 emergency fund.

Frequently Asked Questions

Enter the target amount as FV, annual rate as k, years as n, and 12 for m. The result is the fixed monthly deposit needed. This accounts for each monthly deposit earning interest until the target date.

Monthly saving is generally better because each deposit starts earning interest sooner. The total required monthly savings (multiplied by 12) is slightly less than the equivalent annual deposit, thanks to intra-year compounding.

Use an inflation-adjusted (real) interest rate instead of the nominal rate. Subtract the expected inflation rate from the nominal rate to approximate the real rate. This ensures your goal amount has the same purchasing power in future dollars.