From the initial deposit, final balance, years, and compounding frequency, reverse out the annual nominal rate a savings account must earn.
Input Data
Results
At a glance:The required periodic rate solves finalBalance = initial × (1 + periodicRate)^(m·years); the nominal and effective annual rates derive from it.
Formula
periodicRate = (finalBalance / initial)^(1 / (compoundsPerYear × years)) − 1
nominalRate = periodicRate × compoundsPerYear
effectiveAnnualRate = (1 + periodicRate)^compoundsPerYear − 1
$$F = A \times \left(1 + \dfrac{r}{m}\right)^{m t}$$$$i = \left(\dfrac{F}{A}\right)^{\frac{1}{m t}} - 1, \;\; r = i \times m, \;\; EAR = (1+i)^m - 1$$How to Use
- Enter the initial deposit and final balance.
- Enter the years and compounding frequency.
- Review the nominal, effective, and periodic rates.
FAQ
Is this a pure-principal savings model?
Yes. It uses a single lump-sum compounding model (one deposit, no periodic top-ups) and solves for the rate needed to grow from the initial deposit to the final balance. For regular contributions, use the Investment Calculator instead.
What is the difference between the nominal and effective annual rates?
The nominal rate is simply the periodic rate times the number of compounding periods, ignoring compounding; the effective annual rate (EAR) reflects the real return after interest is reinvested. The higher the compounding frequency, the larger the gap between the two.
Why compare savings products by EAR?
Banks compound at different frequencies; comparing nominal rates alone is misleading. Converting all products to EAR puts them on the same annual footing, so you can fairly compare the true return of various savings or time deposits.
How is the savings interest rate calculator different from the interest-rate and compound-interest calculators — which should I use?
All three centre on principal, rate, term and compounding, but they solve for different unknowns. This Savings Interest Rate Calculator (and the similar Interest Rate Calculator) solves for the rate: you know the initial deposit, final balance, term and compounding, and want the rate needed. Use it to (1) assess a product's true annual return by back-solving from its actual figures, or (2) test whether a savings goal is realistic ('how much rate do I need'). The Compound Interest Calculator runs the opposite direction — given rate, it returns the future value. If you want 'how much will HK$100k at 4% for 5 years become', use Compound Interest. They share the same formula F = A(1+r/m)^(m·t), solving different variables. If your plan involves periodic contributions, use a savings/investment plan calculator that supports them; this reverse model is lump-sum only.
Why are there both a nominal rate and an EAR when I reverse-solve?
They describe the same rate from two angles — the quoted rate versus the real rate. The nominal rate is the periodic rate times the compounding count (the common quoted figure, no compounding effect). The EAR is the true return with compounding: (1 + periodic rate)^count − 1, slightly above the nominal. EAR is higher because compounding means interest earns interest. The more frequent the compounding, the bigger the gap; only annual compounding makes them equal. For comparing products, always use EAR. This calculator shows both for clarity.
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.