The Future Value (FV) Calculator determines the compounded terminal wealth of an initial investment combined with regular monthly contributions over an extended horizon.

### Compounding Equations & Annuity Mathematics The model compounds both a lump-sum initial deposit and a recurring monthly annuity: - **Periodic Interest Rate & Compounding Periods**: $$r = \frac{\text{Annual Rate}}{100 \times 12}, \quad n = \text{Years} \times 12$$ - **Future Value of Lump-Sum Principal**: $$\text{FV}_{\text{lump}} = \text{PV} \times (1 + r)^n$$ - **Future Value of Monthly Deposits (Ordinary Annuity)**: $$\text{FV}_{\text{annuity}} = \text{PMT} \times \left[ \frac{(1 + r)^n - 1}{r} \right]$$ - **Total Portfolio Future Value & Compound Interest**: $$\text{FV}_{\text{total}} = \text{FV}_{\text{lump}} + \text{FV}_{\text{annuity}}$$ $$\text{Total Interest} = \text{FV}_{\text{total}} - [\text{PV} + (\text{PMT} \times n)]$$

### Worked Compounding Example Investing a starting nest egg of $10,000 with monthly additions of $300 over 15 years at an average annual growth rate of 7.0%: - **Total Investment Term**: $15 \times 12 = 180\text{ monthly periods}$ - **Monthly Effective Rate**: $0.07 / 12 \approx 0.0058333$ - **Principal Invested**: $\$10{,}000 + (\$300 \times 180) = \$64{,}000$ - **Lump-Sum Terminal Value**: $\$10{,}000 \times (1.0058333)^{180} \approx \$28{,}489$ - **Annuity Terminal Value**: $\$300 \times \left[ \frac{(1.0058333)^{180} - 1}{0.0058333} \right] \approx \$95{,}099$ - **Total Portfolio Future Value**: $\$28{,}489 + \$95{,}099 \approx \$123{,}588$ - **Earned Compound Interest**: $\$123{,}588 - \$64{,}000 = \$59{,}588$

### Client-Side Processing Notice All financial projections execute locally inside your web browser. No portfolio values, account balances, or savings targets are saved or transmitted to remote servers.