Compound Savings Formula

Finance Formula • Published on September 01, 2026 • Last updated September 01, 2026

Mathematical Equation

$$A = P \times \left(1 + \frac{r}{n}\right)^{nt} + PMT \times \frac{\left(1 + \frac{r}{n}\right)^{nt} - 1}{\frac{r}{n}}$$

Variable Definitions

Total projected future savings balance

Initial starting deposit amount

PMT

Regular periodic contribution deposit amount

Annual interest rate as decimal (Annual Rate / 100)

Compounding & contribution periods per year (e.g. 12 for monthly)

Investment duration in years

Detailed Explanation

In-Depth Guide

The Compound Savings Formula computes the total future wealth accumulated from an initial starting deposit (P) plus regular periodic additions (PMT) earning compound interest over time (t).

How to Calculate: Step-by-Step

1. Calculate future value of starting deposit: $A_{principal} = P \times (1 + r/n)^{nt}$. 2. Calculate periodic rate $i = r/n$ and total periods $k = n \times t$. 3. Calculate future value of regular contributions: $A_{contrib} = PMT \times \frac{(1 + i)^k - 1}{i}$. 4. Add $A_{principal}$ and $A_{contrib}$ to determine total future savings balance ($A$).

Worked Calculation Example

Investing ₹50,000 initial deposit with ₹5,000 regular monthly contributions for 5 years at 7.5% annual interest compounded monthly: - Initial Deposit Growth: $50,000 \times (1 + 0.00625)^{60} = ₹72,497$ - Monthly Contributions Growth: $5,000 \times \frac{(1 + 0.00625)^{60} - 1}{0.00625} = ₹362,803$ - Total Estimated Future Balance ($A$) = ₹72,497 + ₹362,803 = ₹435,300

Common Use Cases

Long-term wealth building & savings projection
Planning monthly recurring deposit growth
Comparing initial lump-sum vs monthly contribution efficiency

Frequently Asked Questions

Compounding monthly reinvests your returns 12 times a year, generating interest on interest for both your initial deposit and every regular monthly addition.

Simple interest is earned only on the initial principal. Compound savings earns interest on your initial principal, your regular additions, and all accumulated interest.

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