Savings Interest Rate Calculator — Find the Return You Need
Know exactly what return your savings need: enter your starting balance, monthly contribution, target balance and time horizon — the calculator finds the required annual interest rate using precision bisection.
years
Nominal annual rate with monthly compounding needed to reach your target
- 1
Monthly rate (from bisection)
0.012751Found by 80-step bisection of FV = PV·(1+r)ⁿ + PMT·((1+r)ⁿ−1)/r — no algebraic closed form exists for r. - 2
Nominal annual rate
0.012751 × 12 × 100 = 15.30
How does this calculator work?
Solves FV = PV·(1+r)^n + PMT·((1+r)^n−1)/r for r via bisection. Reports nominal annual rate (r×12) and effective annual rate ((1+r)^12−1). Enter starting balance, monthly contribution, savings target and years to find the return your plan requires.
Formula
How this is calculated
There is no algebraic closed-form for the interest rate in the compound-annuity formula, so the calculator uses an 80-step bisection (binary search) that converges the monthly rate to more than ten significant figures. The equation being solved is FV = PV·(1+r)^n + PMT·((1+r)^n−1)/r, where r is the monthly interest rate, n is the number of months, PV is the opening balance, PMT is the monthly contribution and FV is the target balance.
Once the monthly rate r is found, the nominal annual rate is r × 12 and the effective annual rate (EAR) is (1+r)^12 − 1. The EAR accounts for monthly compounding and is the figure to compare against annually or quarterly compounded products — it is always slightly higher than the nominal rate.
Limitations: the model assumes end-of-month contributions (ordinary annuity) and a constant rate throughout the horizon. Real savings accounts and investment platforms offer variable or tiered rates; treat this result as a minimum benchmark when comparing products. If the required rate is very high, increasing the monthly contribution or extending the time horizon will bring it down.
Frequently asked questions
The nominal annual rate is simply the monthly rate × 12. The effective annual rate (EAR) accounts for monthly compounding — (1+monthly rate)^12 − 1 — and is always slightly higher. Use the EAR to compare products with different compounding schedules on equal terms.
Increase your monthly contribution or extend the time horizon; both reduce the rate needed to close the gap. If the result still exceeds realistic deposit or investment returns, the shortfall between your savings and goal is too large to bridge with interest alone at your current contribution level.
Monthly is the most common contribution frequency for savings and investment accounts, giving a practical and conservative benchmark. For other frequencies, the effective rate would differ slightly — but the nominal rate here is a good starting point for comparison.
TG we-Calculate Editorial Team. (2026). Savings Interest Rate Calculator — Find the Return You Need [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/savings-interest-rate-calculator
TG we-Calculate Editorial Team. "Savings Interest Rate Calculator — Find the Return You Need." TG we-Calculate. 2026. https://we-calculate.com/calculator/savings-interest-rate-calculator.
TG we-Calculate Editorial Team, "Savings Interest Rate Calculator — Find the Return You Need," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/savings-interest-rate-calculator
@misc{wecalculate_savings_interest_rate_calculator, title = {Savings Interest Rate Calculator — Find the Return You Need}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/savings-interest-rate-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?