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Time to Reach FV Goal

How long to reach a savings goal with periodic deposits.

When to use: Use to find how long monthly or quarterly savings take to reach a goal.

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Formula

n=ln(FV×(k/m)PMT+1)m×ln(1+km)n = \frac{\ln\left(\frac{FV \times (k/m)}{PMT} + 1\right)}{m \times \ln\left(1 + \frac{k}{m}\right)}

Variables

SymbolNameDescriptionUnit
nNumber of YearsTime to reach targetyears
FVFuture ValueSavings goal$
PMTPaymentPeriodic savings amount$
kInterest RateNominal annual rate%
mPeriods/YearDeposits per yearinteger

Real-Life Examples

Example 1: Monthly Savings Goal

Save $500/month at 6% monthly compounding. How long to reach $100,000?

Given

FV = 100,000PMT = 500k = 0.06m = 12

Step-by-Step

1.n = ln(100000 × 0.005/500 + 1) / [12 × ln(1.005)]
2.n = ln(2) / 0.05985
3.n = 0.6931 / 0.05985
4.n = 11.58 years
Result:11.58

About 11.58 years of monthly $500 savings to reach $100,000.

Example 2: Quarterly Investment

Invest $2,000/quarter at 8% quarterly. How long to $200,000?

Given

FV = 200,000PMT = 2,000k = 0.08m = 4

Step-by-Step

1.n = ln(200000 × 0.02/2000 + 1) / [4 × ln(1.02)]
2.n = ln(3) / 0.07921
3.n = 1.0986 / 0.07921
4.n = 13.87 years
Result:13.87

About 13.87 years of quarterly investments to reach $200,000.

Frequently Asked Questions

Enter the target amount as FV, monthly savings as PMT, annual rate as k, and 12 for m. The formula tells you how many years of monthly deposits are needed to reach your goal.

Saving monthly reaches goals slightly faster than saving the equivalent annual amount once per year. This is because monthly deposits start earning interest sooner throughout the year, providing a compounding advantage.

You can increase the periodic deposit amount, find a higher return rate, or contribute more frequently. Increasing the deposit is usually the most impactful and controllable factor.