Savings Goal Formula

Finance Formula • Published on July 30, 2026 • Last updated August 09, 2026

Mathematical Equation

$$PMT = \frac{FV - PV \times (1 + r)^n}{\frac{(1 + r)^n - 1}{r}}$$

Variable Definitions

PMT

Required recurring deposit amount per contribution period

FV

Target savings goal amount (Future Value)

PV

Current initial starting savings balance (Present Value)

r

Periodic interest rate per deposit compounding period (Annual Rate / Periods per year / 100)

n

Total number of deposit periods (Years × Contribution frequencies per year)

Detailed Explanation

In-Depth Guide

The Savings Goal Formula is a reverse sinking fund calculation that computes the exact recurring deposit amount (PMT) required to reach a target future financial goal (FV) within a designated timeline. It factors in starting savings balance (PV), periodic compound interest growth (r), and contribution frequency (monthly, weekly, or annually).

How to Calculate: Step-by-Step

1. Identify your target savings goal amount ($FV$), initial starting balance ($PV$), and target timeline in years. 2. Convert annual interest rate ($R$) to periodic compounding rate ($r = R / (12 \times 100)$). 3. Determine total contribution periods ($n = \text{years} \times 12$). 4. Calculate future value of initial balance: $FV_{PV} = PV \times (1 + r)^n$. 5. Calculate remaining target net amount needed: $FV_{net} = FV - FV_{PV}$. 6. Divide net target by the ordinary annuity factor to determine required periodic deposit ($PMT$).

Worked Calculation Example

Suppose you want to accumulate a ₹1,000,000 target goal in 5 years (60 monthly periods) starting with ₹100,000 initial savings at an 8% expected annual return: - Initial Balance Growth: $100,000 \times (1 + 0.006667)^{60} = ₹148,985$ - Net Target Remaining: $1,000,000 - 148,985 = ₹851,015$ - Annuity Factor: $\frac{(1 + 0.006667)^{60} - 1}{0.006667} \approx 73.476$ - Required Monthly Deposit: $PMT = \frac{851,015}{73.476} \approx ₹11,582\text{ per month}$

Common Use Cases

  • Down payment & home purchase goal planning
  • Emergency fund & retirement sinking fund calculation
  • Multi-goal bucket budgeting & timeline what-if testing

Frequently Asked Questions

If your initial deposit compounded over your timeline exceeds your target future value, the required deposit (PMT) becomes ₹0 because compounding alone hits your goal.

More frequent contributions (such as weekly or monthly instead of yearly) compound earlier, slightly reducing the total money you need to deposit out of pocket.

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