Quick answer: banks choose deposit rates by balancing the value of attracting and retaining funding against the interest expense created by paying more for every deposit that receives the higher rate. The central mathematical question is not “What rate attracts deposits?” but “What rate maximises the value of the whole deposit portfolio after funding value, customer response, product substitution, liquidity needs, interest-rate risk, operating cost and regulatory constraints are included?” The answer changes by product, customer segment and market regime because deposit demand is elastic rather than fixed.

A higher deposit rate buys more funding only if customers respond. It also reprices money the bank may already have.

Exact reader question and page role

This article answers one narrow question: how can a bank mathematically choose a deposit rate rather than merely observe deposit behaviour? It is deliberately separate from How Banks Model Deposit Behaviour, which owns deposit betas, decay and pass-through as behavioural measurements. Here those behavioural estimates become inputs to a pricing decision.

1. Deposit pricing begins with an objective function

Suppose a bank sets rate r on a deposit product. Let D(r) be the expected deposit balance that remains or arrives at that rate. Let V be the economic value per dollar of funding before the customer rate, incorporating the alternative cost of wholesale funding, liquidity value and other governed transfer-pricing components.

A teaching version of deposit contribution is:

Profit(r) = D(r) × [V − r − c] − acquisition/servicing cost(r)

where c represents operating or product costs expressed consistently with the rate. The bank wants the rate where the extra value of retaining or attracting deposits is just balanced by the extra expense of paying that rate.

The formula is intentionally simplified. Real pricing systems can include segmented balances, promotional tiers, optionality, currency, liquidity horizon, cross-product value and behavioural assumptions. The purpose of the model is to expose the trade-off rather than hide it inside a “competitive rate.”

2. Elasticity measures customer response to the rate

Price elasticity of deposits can be written:

ε = (% change in deposit quantity) / (% change in offered rate or relevant rate spread).

For bank deposits the exact denominator needs care because rates can start near zero. Many models therefore use basis-point changes, log transformations, spreads to a market benchmark, or discrete-choice formulations rather than a naive percentage elasticity.

If an extra 25 basis points retains little additional money, the bank may be paying more on the whole book without buying much incremental funding. If the same move materially reduces attrition in a highly rate-sensitive segment, the economics can reverse.

3. Current evidence shows that responsiveness differs by bank and product

A BIS Working Paper published on 8 June 2026 finds that US digital banks generally pay higher deposit rates than traditional banks and adjust them more strongly to monetary-policy changes, with responsiveness differing by product. The study also finds that stronger information flow through social media can intensify deposit-price competition. See The digitalisation of banking and social media: implications for deposit pricing.

The lesson is algorithmic: a single “industry deposit beta” is unlikely to be enough for pricing. Channel, product, customer attention and competitive environment can change the response function D(r).

4. Deposit beta and pricing elasticity are related but not identical

A deposit beta measures how an offered deposit rate changes relative to a benchmark such as the policy rate:

Deposit beta ≈ Δ deposit rate / Δ benchmark rate.

Pricing elasticity asks how customers respond to the rate that the bank chooses. One describes the bank’s historical repricing behaviour; the other describes the customer-demand function faced by the bank.

Confusing them creates a circular model: “we raised rates because customers were rate-sensitive, and we know customers were rate-sensitive because we raised rates.” A better system estimates customer response from controlled variation, natural experiments, segment comparisons or carefully governed causal methods.

5. The marginal-cost problem: repricing old money to win new money

Suppose a savings product holds S$1 billion at 2.00%. Management estimates that raising the rate to 2.10% will attract S$20 million of additional deposits.

If the higher rate applies to the entire existing S$1 billion plus the new S$20 million, annual interest expense rises by roughly:

0.10% × S$1.02bn = S$1.02m.

The bank paid about S$1.02 million more to obtain only S$20 million of incremental funding. The marginal funding cost of that new S$20 million is therefore far higher than ten basis points unless existing balances would otherwise have left.

This is one of the most important deposit-pricing corrections: average customer rate and marginal cost of incremental deposits are different quantities.

6. Attrition turns retention into a survival model

Instead of modelling only the total balance, a bank can model the probability that an account or balance survives:

P(stays beyond t | rate gap, tenure, balance, channel, product, customer features, market state).

This can be implemented with hazard models, logistic regression, gradient boosting or other validated methods. The key output is not merely “rate-sensitive customer” but a conditional retention curve.

A model should distinguish voluntary switching, normal spending withdrawals, seasonal cash needs and bank-initiated account changes. Otherwise ordinary payment behaviour can be misclassified as price attrition.

7. Funding value comes from the alternative the deposit replaces

Deposits are valuable partly because they fund assets. But one dollar of deposits is not automatically worth one fixed amount. Value can depend on expected life, stability, currency and the alternative funding source it replaces.

A treasury transfer-pricing system can provide an internal value V for the deposit’s funding and liquidity characteristics. See How Banks Use Funds Transfer Pricing Algorithms.

If alternative term funding is expensive, stable deposits can have high marginal value. If the bank already has excess liquidity and little profitable asset demand, paying aggressively for additional deposits can destroy value even if balances grow.

8. Cannibalisation: the deposit may come from another product inside the same bank

A bank launches a high-rate savings account and attracts S$100 million. If S$80 million moved from its own lower-rate transaction accounts, net new funding is only S$20 million.

Define a simple cannibalisation share:

C = internal migrated balance / gross balance gained.

High C means the campaign mainly repriced existing funding rather than attracting new funding. This can still be rational if it prevents those balances from leaving the bank entirely, but the model must classify the counterfactual correctly.

9. Customer segmentation should be causal, not cosmetic

Pricing models often segment customers by balance, tenure, digital engagement, transaction activity, product mix or observed rate sensitivity. Segmentation is useful only if the groups genuinely respond differently or create different economic value.

A dangerous model creates many segments, observes small historical differences and then treats every difference as stable. This is overfitting. Segment rules should survive out-of-time testing and remain large enough for credible estimation.

10. A discrete-choice model can represent competition directly

Instead of predicting balance mechanically, a bank can model the probability that a customer chooses among products or institutions:

P(choice=j) = exp(U_j) / Σ exp(U_k)

where utility U can include rate, convenience, digital experience, branch access, switching friction and relationship features.

This makes the competitive problem explicit: the customer is not deciding whether to hold deposits in a vacuum but choosing among alternatives whose prices also move.

11. Rate tiers create nonlinear optimisation

Many products pay different rates by balance tier or require conditions such as salary crediting, spending or bundled relationships. The pricing variable becomes a vector rather than one rate:

r = [r₁, r₂, …, r_n].

The bank must forecast how customers distribute balances across tiers and whether a threshold causes bunching. Sharp thresholds can create unexpected migration because customers rationally move just enough money to qualify for the higher rate.

12. Regulatory and liquidity constraints bound the optimum

The unconstrained profit-maximising rate is not necessarily an admissible rate. In the United States, less-than-well-capitalised institutions face restrictions tied to national and local rate caps. The FDIC publishes national rates and rate caps under its current rule. See FDIC National Rates and Rate Caps.

More broadly, deposit pricing must fit liquidity, interest-rate-risk, conduct and product-governance frameworks. A high rate that attracts volatile funding can improve one metric while worsening another.

Structural funding constraints also matter. See How Banks Calculate and Optimise the Net Stable Funding Ratio.

13. The constrained optimisation problem

A stylised bank can solve:

Maximise Σ segment contribution(r) − concentration penalties − volatility penalties

subject to constraints such as:

required total funding ≥ target;
liquidity metrics within limits;
interest-rate-risk exposure within limits;
product rates within legal/governance bounds;
customer eligibility rules consistently applied;
concentration in rate-sensitive or uninsured balances below risk appetite.

The solution is a rate vector, not a universal “best deposit rate.”

14. Failure modes

Average-cost blindness. The bank ignores the cost of repricing existing balances to attract a small incremental amount.
Deposit-beta substitution. Historical bank repricing is mistaken for customer elasticity.
Cannibalisation blindness. Internal migration is counted as new funding.
Competitor-static assumption. Other banks’ rates are treated as fixed while the bank changes its own.
Segment overfit. Tiny historical groups are treated as stable pricing populations.
Liquidity-value inflation. Every additional deposit is assigned high funding value even when the bank already has excess liquidity.
Attrition label error. Ordinary spending or seasonal withdrawals are mistaken for rate-driven switching.
One-regime calibration. Elasticity from a low-rate era is carried unchanged into a high-information digital market.

15. Counterexamples and falsifiers

Claim: “Raising the rate always increases deposit profitability.” Falsifier: the extra rate applies to a large existing book while incremental balances are small, making marginal funding cost exceed the value of new funding.

Claim: “The highest-rate bank will win the most stable deposits.” Falsifier: balances attracted primarily by rate can leave quickly when competitors reprice, while lower-rate relationship deposits remain.

Claim: “A campaign generated S$100m of deposits.” Falsifier: account-level tracing shows S$80m came from another product at the same bank.

16. Diagnostics

What is the incremental balance gained per basis point?
How much of gross growth is internal cannibalisation?
What is the marginal funding cost of the incremental balance?
Which segments show statistically credible rate response?
How quickly do promotional balances leave after the offer ends?
Does elasticity change when competitor rates move at the same time?
How much of deposit value comes from liquidity versus spread income?
Does the rate decision remain optimal under stress runoff assumptions?

17. Verification and update triggers

backtest predicted balance response against realised balances;
separate new-to-bank funds from internal migration;
run holdout tests across rate regimes;
compare complex elasticity models with simple segment baselines;
re-estimate after major competitor or digital-channel changes;
reprice the funding-value input when wholesale funding curves move;
revalidate after product redesign or eligibility changes;
monitor whether customers who arrive for rate remain after the rate advantage disappears.

18. Alternatives to changing the headline rate

If the bank needs more stable funding, rate is only one control. Alternatives include changing maturity, offering term deposits, improving service, simplifying onboarding, changing product bundles, reducing unnecessary friction, or altering asset growth so less marginal funding is required.

That final alternative matters. The cheapest deposit is not automatically the best solution if the bank can reduce a low-return asset position instead. This connects deposit pricing to balance-sheet optimisation.

Research anchors

The deeper mathematical lesson

Deposit pricing is an optimisation problem with feedback. The bank changes a rate; customers respond; competitors respond; balances migrate; funding value changes; the next pricing decision starts from a new state. The strongest model therefore does not search for a permanently correct rate. It estimates a response function, calculates marginal value, checks the counterfactual, and keeps updating when the market proves the old elasticity wrong.

Educational boundary: This article explains banking mathematics and computational decision-making. It is not a recommendation about where to deposit money, which bank to use, or what rate any individual should accept.

Small Group Tutorials

How Banks Choose Deposit Rates: Price Elasticity, Customer Attrition, Funding Value, Cannibalisation and Constrained Optimisation