How to use Finance vs Cash

Pay cash, or borrow and keep your cash earning? This guide shows how to set up a purchase and its loan offers, then how the tool decides. Every demo on this page is the real tool, running live in your browser. Press Pause on one to try it yourself.

The short version

  1. Load or enter a purchase

    Start from a worked comparison in Quick Start, or enter the cash price, the cash you have, and the Risk-Free Rate your spare cash earns.

  2. Describe each loan offer

    One tab per offer on Loan offers: its loan type, term, rate, down payment and fees. A gauge beside a field sweeps it with Optimise.

  3. Simulate and read

    Press β–Ά Simulate. The verdict names the best strategy and its Net Benefit vs Cash; the chart and the tables below give the detail.

Nothing is uploaded. Every figure is worked out in your browser, and your plan is kept in this browser only. This guide is general information, not financial advice.

The screen

Inputs on the left, the answer beside them, then the chart and the tables under it. Point at a part in the list to see where it is.

  1. Inputs

    Quick Start, save and open, then three tabs: Purchase, Loan offers and Assumptions. β–Ά Simulate sits at the bottom. The chevrons fold the card to a slim Inputs rail.

  2. The answer

    The verdict in a sentence, Show in today's money, then four figures: Best Strategy, Net Benefit vs Cash, Total Interest (Best) and Cash Purchase Wealth.

  3. Chart

    Each offer and the cash purchase over time, read as Ending Wealth, Net Benefit, Investment Value or Loan Balance. Share sits above it.

  4. Tables

    Scenario Comparison, every figure side by side; the Amortization Schedule, one row per repayment; and What this assumes.

Top right, Tour replays a one minute walk through the tool, and Guide opens this page.

Quick Start

Six worked comparisons, each a decision people really face: a House, fixed vs float, a Car, 3yr or balloon, a Phone on a plan that quotes no rate, a Credit card 0% conversion, a Motorbike, flat rate, and Furniture, pay later. One click fills every tab and runs it.

On a phone, press Full screen under a demo and turn the phone sideways to read it.

Open the inputs, load the car
  1. Open the inputs

    On a first visit the card is folded to a rail, so the answer has the room. Click Inputs to open it; it stays the way you leave it.

  2. Pick a comparison

    Hover a button to read what it holds and what it teaches. A click loads it and runs it.

  3. Read the answer

    The verdict and Net Benefit vs Cash: for the car, every loan trails paying cash, the three-year one by the least.

  • A Quick Start is also the reset. Each one is built from the same defaults, not from what is on screen, so it clears the plan before it.
  • Each one carries a lesson. The car's smallest instalment (the balloon) finishes last; the motorbike's 0.9% a month flat costs 21.03% a year; the furniture's payment holiday grows the debt.

The purchase

The Purchase tab holds what both paths share: the price, the cash you have today, and the symbol money is shown in. Typing never reruns the answer; β–Ά Simulate does.

A $45,000 purchase with $60,000 on hand
  1. The price and your cash

    Cash Purchase Cost is what paying in full costs. Available Cash is what you hold today; it must cover the price.

  2. A price per offer

    Price Each Loan Offer Separately gives each offer its own price, as an amount, a % of cash or a % off.

  3. Simulate

    An edit sends the board out of date and says so above the button. β–Ά Simulate runs every offer against cash.

  • Cash below the price is not modelled. The tool compares financing against genuinely paying cash, so the board stays blank and says why.
  • The currency is a label. Nothing is converted.

Loan offers

Each offer is a tab on the bar. The form under it is that offer, in titled sections: Loan Structure, Repayment Term, Interest Rate (or Repayment Plan for a known repayment), then Upfront & Fees. Every edit applies as you make it.

The car's offers, and a flat-rate one beside them
  1. One tab per offer

    Click a tab to edit it, double-click to rename it, click its dot to recolour it. The icons beside the bar duplicate or remove the one on screen.

  2. Add an offer

    + adds one: an amortizing loan at 5% over 60 months, 0% down.

  3. Its loan type

    Loan Type picks one of seven structures. The fields below change to suit it.

  4. Term, rate and fees

    Term counts repayments, Finance Rate is yearly, then the Down Payment, Origination Fee, Fee Treatment and Admin Fee.

  5. Simulate

    The new offer joins the comparison. A 4.9% flat rate shows as 9.32% in Effective Rate (APR).

  • Learn more β†— under Loan Type opens Loan Types Explained: each structure with its formula, the markets it is sold in and a worked example.
  • Repayment Frequency converts the term when it changes: 60 months becomes 260 weeks, the same five years.

Loan types with a field of their own

Some structures bring a field: Interest-Only or Payment Holiday periods, a Residual, a Repayment Amount instead of a rate. And any rate that can move takes a Rate Basis of Schedule.

A phone plan's solved rate, then a house loan that floats
  1. Known repayment

    For a plan that quotes an instalment and no rate: enter the Repayment Amount, one figure or a stepped Schedule.

  2. The rate it implies

    Implied Rate is the yearly rate that repays the loan exactly. 24 payments of $82 on $1,800 is 9.08%; of $78, 3.86%.

  3. Fixed, then floating

    A Rate Schedule is consecutive periods, each Fixed or Floating between a min and a max. Here: two years at 5.80%, then 5% to 8.5%.

  4. The band

    A floating rate runs three times, at its min, middle and max. The chart shades the range; the tables use the middle.

  • A flat rate and a known repayment take no schedule. A flat loan fixes its interest at the start; a known repayment has the rate as its answer.
  • No rate repays it? A repayment too small for any rate is skipped, and the banner says to raise it or shorten the term.

Assumptions

What your spare cash earns, how a quoted loan rate is read, and how fast prices rise. The first is the yardstick every offer is measured against.

The car at 6% risk-free, nominal rates, 3% inflation
  1. Risk-Free Rate

    What cash earns in a safe place, such as a savings account. Every offer and the cash purchase use it.

  2. Rate Convention

    Effective annual (EAR) compounds a loan rate down to each repayment; Nominal annual (APR) divides it. Loans only, never the cash rate.

  3. Inflation

    Never changes a loan or the cash. The note under it says what the price costs at the end.

  4. Show in today's money

    Beside the results: every figure divided by inflation up to its own date. Off again, every figure is back to the cent.

The answer

The verdict names the best strategy and by how much it beats, or trails, paying cash. The four figures under it say the same in numbers, and the Scenario Comparison shows how each offer got there.

The opening plan, with cash earning 6%
  1. The verdict

    The best strategy, its Net Benefit vs Cash and when, and its effective rate against the Risk-Free Rate. Here the 5% loan beats cash by $1.5k.

  2. Four figures

    Net Benefit vs Cash: above zero, financing wins. Cash Purchase Wealth: the cash left after paying in full, grown at the risk-free rate.

  3. Optimization Target

    Which offer counts as best: Highest Net Benefit, Lowest Total Interest or Lowest Financing Cost. The 7% loan pays $1,059 less interest, yet trails cash by $842.

  4. Scenario Comparison

    Every figure per offer, each at the end of its own term, against cash over the same time.

  • Banners say what to doubt. Negative carry: a loan's effective rate is above the risk-free rate. Negative amortization: a repayment is below the interest due, so the balance grows.
  • What this assumes, the last card, lists what the answer rests on for this plan: the cash, the rates, the fees, the horizon.

Chart and schedule

The chart puts every offer and the cash purchase on one time axis, in the finest repayment period on show. The Amortization Schedule under the table gives one row per repayment.

Furniture, pay later: the debt climbing through the holiday
  1. Chart Metric

    Ending Wealth (cash kept less debt), Net Benefit, Investment Value or Loan Balance.

  2. Read a date

    Hover the chart and the line under it reads every series at that date.

  3. Amortization Schedule

    Opens from its chevron. One tab per offer: start balance, interest, principal, payment, end balance. ⬇ CSV saves it.

  • Scroll or pinch to zoom, drag to pan, ⟳ to reset. Past an offer's term its cash keeps compounding at the risk-free rate, so shorter offers line up with longer ones.

Optimise

The gold gauge beside a field sweeps it over a range on the offer on screen, up to two settings at once. The board then shows the best tested setting, your current one and the worst, each beside the cash purchase.

The car's three-year loan, over 12 to 60 months
  1. Pick a setting

    Click the gauge beside Term, Finance Rate, Down Payment, a fee, the Risk-Free Rate and more.

  2. Set the range

    Start value, End value and Steps, the values tested. βœ“ Done keeps it.

  3. β–Ά Optimise

    Simulate becomes β–Ά Optimise, and the note above it says what will run.

  4. Best, yours, worst

    Three tiles and the cash purchase. The chart plots the Objective against the setting; two settings draw a surface.

  5. Back to comparing

    Cancel drops the sweep, and β–Ά Simulate compares every offer again.

  • One offer, every combination. Up to 50 values a setting and 2,500 runs, all on the same engine as Simulate. The Objective can be Net Benefit, Ending Wealth, Total Interest, Total Financing Cost or Effective Rate.
  • Left out on purpose: the loan type, the frequency and the rate and repayment bases, since each swaps the fields around it.
  • The best is the best on these inputs, not a forecast. It moves when the cash, the rates or the price do.

Save, export and share

The tool keeps your plan in this browser between visits. The rest makes something to keep or send.

Save, open and Share
  1. Save or open a file

    The two icons beside Quick Start write the whole plan, every offer included, to a file, and read one back.

  2. Share

    The chart as SVG or PNG, a copy to the clipboard, a link that opens the tool on your plan, or an embed for a web page.

  • An embed is live. It shows the chart as you drew it, and a reader can hover and zoom it.
Part 2

How the numbers work

What each field means, where it enters the calculation, and what moving it does to the answer. Every formula here is the one the tool runs.

The model in one picture

Both paths start from the same cash. Paying cash spends the price today and leaves the rest earning the risk-free rate. Financing spends only the down payment and any upfront fee today, keeps the rest earning the same rate, and pays each repayment out of it. The tool compares what each path holds at the end of the offer's term, once the loan is repaid.

Financing W0 = A βˆ’ D βˆ’ F0,   Wk = Wkβˆ’1 Γ— (1 + i) βˆ’ Rk βˆ’ aeach repayment period
Paying cash Wcash = (A βˆ’ C) Γ— (1 + i)n
Net Benefit vs Cash = Wn βˆ’ Wcash = (1 + i)n Γ— [ (C βˆ’ D βˆ’ F0) βˆ’ Ξ£ Rk + a(1 + i)k ]
  • AAvailable Cash
  • CCash Purchase Cost
  • Dthe down payment, a share of the offer's price
  • F0an origination fee Paid upfront from cash (else 0)
  • Rkrepayment k of n, set by the loan type
  • athe Admin Fee on every repayment
  • ithe Risk-Free Rate per period: (1 + rf)1/m βˆ’ 1, with m repayments a year
  • nthe number of repayments, the Term
  • Read the bracket as a present value. It is what financing lets you keep today, less what everything you pay later is worth today at the rate your cash earns. The tool carries that forward to the end of the term, so Net Benefit is in the money of that date.
  • The wash. Borrow at exactly the rate your cash earns, with no fee, and the repayments are worth exactly the loan: Net Benefit is zero for every loan type, frequency, term and down payment. Measured on the car's three-year loan at 4.5% with its fee removed: $0.00.
  • So the rule is one comparison. With no fees and the offer at the cash price, financing wins exactly when the loan's Effective Rate (APR) is below the Risk-Free Rate. Fees count against it, and a cheaper offer price counts for it.
  • Timing. The cash grows for a period first, then the repayment comes out of it. The first repayment falls one period after the purchase, and the last one clears the loan exactly.
  • Each offer is scored at the end of its own term, against paying cash over the same time. Best Strategy is the top offer by the Optimization Target, or Cash Purchase when every Net Benefit is below zero.
FigureWhat it isIn the maths
Ending WealthThe cash still invested at the end of the term, less any debt.Wn. On the chart over time: invested cash βˆ’ loan balance.
Cash Purchase at Same HorizonThe cash left after paying in full, grown to the offer's own end date.Wcash. The Cash Purchase Wealth tile runs it to the longest offer.
Net Benefit vs CashHow much better off financing leaves you. Below zero, paying cash is better.Wn βˆ’ Wcash. A difference under half a cent reads as a tie.
Effective Rate (APR)What the loan really costs a year, whatever its shape.The rate r that makes the repayments repay the amount financed, as (1 + r)m βˆ’ 1. An effective annual rate, and it leaves fees out.
Total Interest PaidAll the interest over the term.Ξ£ interestk. No fees in it.
Total Financing CostWhat borrowing costs, before any credit for the cash it keeps.Total interest + origination fee + a Γ— n.
Total Out-of-PocketEvery dollar handed over.D + F0 + Ξ£ Rk + a Γ— n. A fee inside the loan is in the repayments, counted once.

Watch out. Total Financing Cost and Total Out-of-Pocket ignore what your cash earns meanwhile, so they always favour paying cash. A 0% plan with no fee costs $0 and is still better than cash, because the cash you keep earns interest. Net Benefit is the only figure that counts both sides.

Purchase

The price and the cash. Surprisingly, the cash you hold does not move the answer at all, as long as it covers the price.

An offer at its own price Net Benefit = Net Benefitat price Pβ€² + (C βˆ’ Pβ€²) Γ— (1 + i)n
  • Pβ€²the offer's price: C unless Price Each Loan Offer Separately is on
  • C βˆ’ Pβ€²a discount the financing side keeps invested and the cash buyer never gets
FieldWhat it isIn the mathsRaise it
Currency SymbolThe symbol money is shown in.Nowhere. Nothing is converted.no effect
Cash Purchase CostWhat paying in full costs today.C. Paying cash spends it; financing borrows it less the down payment, so it scales the loan.β–² amount borrowedβ–Ό Net Benefit

While the loan costs more than cash earns. Car, three-year loan: +10% is βˆ’$260.

Price Each Loan Offer SeparatelyGives each offer its own Offer Price.Off, Pβ€² = C for every offer. On, each offer states Pβ€² as an amount, a % of cash or a % off. Cash is always scored at C.a choice
Available CashCash on hand today.A. Must be at least C. The surplus earns the same in both paths and cancels out of Net Benefit.β–² both wealth linesno effect on Net Benefit

Car: Β±10% is $0.

Watch out. More cash in the bank does not make borrowing smarter. It raises Ending Wealth and Cash Purchase Wealth by the same amount, and Net Benefit not at all. What decides it is the loan against the risk-free rate.

Loan offers: the loan structure

The loan type sets the repayments Rk. Every type builds the same rows (start balance, interest, principal, payment, end balance), and the last repayment always clears what is left. Loan Types Explained walks through each one with charts.

Each period interestk = Bkβˆ’1 Γ— r,   Bk = Bkβˆ’1 + interestk βˆ’ Rkall but the flat rate
  • Bkthe balance after repayment k; B0 = L, the amount financed
  • rthe loan rate per period (see term and rate)
  • n, kthe term, and the repayment being made
Loan TypeWhat you payIn the mathsNext to amortizing
AmortizingOne equal instalment; interest on what you still owe.
R = L Γ— r(1 + r)n(1 + r)n βˆ’ 1

At 0%, R = L Γ· n. Re-worked over the remaining term whenever the rate changes.

the standard
Flat rateInterest on the original amount for the whole term.
R = L Γ· n + L Γ— r

Total interest = L Γ— r Γ— n. The first period's rate holds for the whole loan.

β–² effective rate, about double

Motorbike: 10.8% flat is 21.03% effective; amortizing, 11.35%.

Interest-onlyInterest alone for the Interest-Only periods, then instalments.Rk = B Γ— r for k ≀ q, then amortizing over the rest. q = n repays all the principal at the end.β–² balance carried longer

Magnifies the spread, whichever way it runs.

Balloon / residualSmaller instalments, with the Residual due in a lump at the end.
R = (L βˆ’ ρL(1 + r)n) Γ— r(1 + r)n(1 + r)n βˆ’ 1

Final payment = R + ρL, with ρ the residual share.

β–Ό instalment, β–² interest

Car: $630.55 a month, then $14,805.55; 5 years, βˆ’$6,444 against βˆ’$5,162.

Known repaymentThe instalment you were quoted, one figure or a stepped schedule.Solves r so that Bn = 0, by bisection. Implied Rate = (1 + r)m βˆ’ 1. A repayment below the interest due grows the debt, and the tool says so.rate is the answer

Phone: 12 Γ— $150 on $1,800 is 0%; 36 Γ— $57 is 9.07%.

BulletNothing until maturity, then all of it.Interest is added to the debt every period; one payment of L(1 + r)n at the end.β–² balance carried longest
Deferred startA Payment Holiday, then normal instalments.Bh = L(1 + r)h after h holiday periods, then amortizing over n βˆ’ h. Interest is added to the debt meanwhile, so the balance rises above the amount borrowed.β–² debt during the holiday

Furniture: $6,000 grows to $7,194 before the first payment.

FieldWhat it isIn the mathsRaise it
Loan TypeThe repayment structure the lender sells.Picks the formula for Rk above.a choice of structure
Interest-Only / Payment HolidayHow many repayments run before normal instalments begin.q or h. Capped at the term.β–² balance carried longerβ–Ό Net Benefit

While the loan costs more than cash earns.

ResidualThe share of the amount financed still owed at the end.ρ, 0% to 99% of L.β–Ό instalmentβ–Ό Net Benefit

While the loan costs more than cash earns.

Watch out. A flat rate is not comparable with an ordinary rate. You keep paying interest on money you have already repaid, so the average balance is about half the loan while the interest is charged on all of it. Compare Effective Rate (APR), never the quoted figure: the motorbike's 0.9% a month flat costs nearly twice its 10.8% amortizing twin.

Not modelled: deferred interest. Some 0% promotions charge all the back interest if the balance is not cleared by a date. The tool has no such switch. Its 0% plans are amortizing loans at 0%, with any conversion fee as an origination fee.

Loan offers: term and rate

How often you repay, for how long, and at what rate. A yearly rate becomes a rate per repayment one of two ways, set on the Assumptions tab.

Effective (EAR) r = (1 + Ryr)1/m βˆ’ 1the default
Nominal (APR) r = Ryr Γ· m
  • Ryrthe Finance Rate (or a schedule band), a year
  • mrepayments a year: 52, 26, 12 or 1
  • rthe rate charged each repayment period
FieldWhat it isIn the mathsRaise it
Repayment FrequencyWeekly, fortnightly, monthly or yearly.m, in the loan's r and the cash's i. Switching converts the term, so the years stay the same.β–² repaid sooner

Car: weekly is +$57; yearly, βˆ’$836, since each payment waits a year.

TermThe number of repayments.n. How long the loan runs, and how long the spread between loan and cash runs.β–Ό instalmentβ–Ό Net Benefit

While the loan costs more than cash earns. Car: 48 months is βˆ’$1,012; 24 months, +$936.

Rate BasisSimple, one rate; or Schedule, periods that each hold a rate.Picks Finance Rate or Rate Schedule. Not for a flat rate or a known repayment.a choice
Finance RateThe yearly rate the lender quotes. Flat Rate on a flat loan, Interest Rate on a bullet.Ryr, made r by the convention.β–² repaymentsβ–Ό Net Benefit

Car: +1 point is βˆ’$667.

Rate ScheduleConsecutive periods from the first repayment, each Fixed or Floating between a min and a max. The last stretches to the term.Each band sets r for its repayments; the instalment is re-worked on the balance at each change. A floating band runs at its min, middle and max. A payment holiday's schedule starts after the holiday.β–² a band, β–Ό Net Benefit

House, 2 years fixed then 5% to 8.5%: Ending Wealth from βˆ’$321k to +$18k, in today's money.

Repayment BasisKnown repayment only: Single amount or a stepped Schedule.Picks the stream R1 … Rn the rate is solved from.a choice
Repayment Amount / ScheduleWhat you hand over each period.Rk, given; r is solved from it.β–² Implied Rateβ–Ό Net Benefit
Implied RateThe rate the plan works out to. Read only.(1 + r)m βˆ’ 1, an effective annual rate.an answer, not an input

Watch out. A longer term is only worse while the loan costs more than your cash earns. Below the risk-free rate it is better, because cheap debt is kept longer. At exactly the risk-free rate, the term stops mattering.

Loan offers: upfront and fees

What leaves your cash on day one, and what each fee costs once the cash it takes would have earned interest.

Down payment D = d Γ— Pβ€²,   financed base L = Pβ€² βˆ’ D
Amount financed L (paid upfront)  Β·  L + F (added to the loan)  Β·  L1 βˆ’ f (deducted from the advance, a % fee)
What a fee costs F0 Γ— (1 + i)n  +  a Γ— Ξ£ (1 + i)nβˆ’koff Net Benefit
  • dthe Down Payment share
  • F, fthe Origination Fee, as money or as a % of L
  • athe Admin Fee a repayment
FieldWhat it isIn the mathsRaise it
Offer PriceWith a price per offer on: what this offer charges.Pβ€²: an amount, C Γ— % of cash, or C Γ— (1 βˆ’ % off).β–Ό Net Benefit

Furniture: 10% off cuts the loss from βˆ’$2,172 (the holiday) to βˆ’$682.

Down PaymentThe share of the price paid on day one. 100% is paying cash.D, out of W0; the loan shrinks by the same. At 100% there is no loan and Net Benefit is 0.β–Ό amount borrowedβ–² Net Benefit

While the loan costs more than cash earns. Car: 20% is +$289.

Origination FeeA one-off lender's fee, as money or a %.F or f. Never counted as interest.β–Ό Net Benefit

Car: $400 costs $456 by year three, 400 Γ— 1.045Β³.

Fee TreatmentPaid upfront from cash, Added to the loan or Deducted from the advance.Upfront: F0 = F. Inside the loan, the fee is repaid with interest at the loan rate, never counted twice. Deducted, a % fee is grossed up so the net advance still meets the price.a choice

Car: inside the loan costs $26 more, the fee borrowed at 8.4% instead of paid from cash earning 4.5%.

Admin FeeA fixed fee on every repayment, such as account-keeping.a, out of the cash with each Rk. Total = a Γ— n.β–Ό Net Benefit

Car: $10 a month is βˆ’$384.

Watch out. Effective Rate (APR) is the contract rate of the repayments and leaves fees out, in every treatment. A 0% plan with a 3% fee still reads 0.00%. The fee is priced in Total Financing Cost and in Net Benefit: the card's six-month plan finishes last on it.

Assumptions

The risk-free rate is the opportunity cost of your cash: what it would have earned if you had not spent it. It grows the kept cash and, through the identity above, discounts every repayment.

Cash per period i = (1 + rf)1/m βˆ’ 1always effective
Today's money xtoday = x at t years(1 + Ο€)t
  • rfthe Risk-Free Rate, a year
  • Ο€Inflation, a year
FieldWhat it isIn the mathsRaise it
Risk-Free RateWhat spare cash earns in a safe place.i, in both paths. Untaxed, compounded once each repayment period.β–² Net Benefit

Whenever you borrow. Car: +1 point is +$626.

Rate ConventionEffective annual (EAR) or Nominal annual (APR).How a loan's yearly rate becomes r. Never the cash rate, which is always effective.nominal: β–² cost, β–Ό Net Benefit

Car: nominal is βˆ’$221; 8.4% charged 0.70% a month, not 0.67%.

InflationHow fast prices rise.Ο€, only when reading in today's money. Never touches a loan or the cash.no effect on the run
Show in today's moneyThe switch beside the results.Divides each figure by (1 + Ο€)t at its own date; a total is the sum of its parts each read that way. The purchase-day figures stay as they are.a reading, not a model

Watch out. The risk-free rate is not what an investment portfolio might return. If you would put the kept cash in shares, a higher rate would flatter financing, but with a risk the tool does not show. Use what the cash would really earn, safely, after tax.

Worked example

The Car, 3yr or balloon Quick Start's first offer, by hand. Every figure below is the one the tool prints.

Car: $45,000, three-year loan, 10% down

$60,000 on hand, 8.40% a year, 36 monthly repayments, a $400 fee paid upfront, 4.50% risk-free, Effective annual.

  1. Down payment10% Γ— $45,000$4,500
  2. Amount financed$45,000 βˆ’ $4,500$40,500
  3. Loan rate a month1.0841/12 βˆ’ 10.6744%
  4. Instalment$40,500 Γ— 0.006744 Γ— 1.006744³⁢ Γ· (1.006744³⁢ βˆ’ 1)$1,270.86
  5. Total interest36 Γ— $1,270.86 βˆ’ $40,500$5,250.97
  6. Cash kept today$60,000 βˆ’ $4,500 down βˆ’ $400 fee$55,100
  7. Cash rate a month1.0451/12 βˆ’ 10.3675%
  8. Kept cash, grown$55,100 Γ— 1.045Β³$62,878.25
  9. Repayments, grown$1,270.86 Γ— (1.045Β³ βˆ’ 1) Γ· 0.003675βˆ’$48,819.52
  10. Ending Wealth$62,878.25 βˆ’ $48,819.52, the loan now repaid$14,058.74
  11. Cash at the same horizon($60,000 βˆ’ $45,000) Γ— 1.045Β³$17,117.49
  12. Net Benefit vs Cash$14,058.74 βˆ’ $17,117.49βˆ’$3,058.76
  • The same answer as a present value. At 0.3675% a month the 36 instalments are worth $42,780.38 today. Financing kept $40,100 ($45,000 βˆ’ $4,500 βˆ’ $400). The gap, βˆ’$2,680.38, grown 1.045Β³, is βˆ’$3,058.76.
  • Why it loses. The loan costs 8.40% while the kept cash earns 4.50%. On about $40,000 for three years that spread is the loss, plus the fee.

What moves the answer

The same loan, with one input moved down and then up and the rest left as the Quick Start sets them. Measured on the tool itself.

Net Benefit vs Cash, car three-year loan, when one input movesBase case: the Car Quick Start's "3yr loan, 10% down", Net Benefit βˆ’$3,059. Steps: 1 point on a rate, 12 months on the term, 10 points on the down payment, 10% on the price and the cash, $400 on the fee.
Input loweredInput raised
  1. Term36 β†’ 24 / 48 months+$936βˆ’$1,012
  2. Finance Rate8.4% β†’ 7.4% / 9.4%+$667βˆ’$667
  3. Risk-Free Rate4.5% β†’ 3.5% / 5.5%βˆ’$608+$626
  4. Origination Fee$400 β†’ $0 / $800+$456βˆ’$456
  5. Down Payment10% β†’ 0% / 20%βˆ’$289+$289
  6. Cash Purchase Cost$45,000 β†’ $40,500 / $49,500+$260βˆ’$260
  7. Available Cash$60,000 β†’ $54,000 / $66,000$0$0

Read it from the top: the longest bar is the input your answer rests on most. Measured by financingvscash/guides/_sensitivity.mjs.

  • The spread decides the sign; the term and the amount decide the size. Term tops the chart because it is how long a loan costing 3.9 points more than cash runs. The finance rate and the risk-free rate move the answer almost equally and in opposite directions: only the gap between them counts.
  • No single plausible move rescues this loan. Each bar is at most about $1,000 against a $3,059 loss. It draws level with paying cash only at a Finance Rate of about 3.81%, below the 4.5% risk-free rate because the $400 fee must be earned back too.
  • The cash in the bank does nothing. Its bar is empty: the surplus earns the same either way.
  • For your own decision: argue about the rates first, then the term. If your loan's effective rate is well above what your cash safely earns, a shorter term or a bigger down payment loses less, but paying cash still wins.

The longest bar, live: the same loan over a year more, then a year less, with Net Benefit on the chart.

The car's three-year loan over 48 months, then 24
  1. The base case

    Net Benefit βˆ’$3.1k after 36 months. The chart shows each loan's lead over cash over time, below zero all the way.

  2. A longer term

    48 months: a smaller instalment, but a year more of the spread. Net Benefit βˆ’$4.1k.

  3. A shorter term

    24 months: a bigger instalment, a year less of the spread. Net Benefit βˆ’$2.1k.

What it leaves out

The comparison is clean because it holds a lot still. Know what that is before you act on it.

  • The item itself. It costs the same either way, so what it is later worth is left out of both paths. A car that is worth less on a loan (insurance, a lien) is not modelled.
  • Tax. The cash earns the risk-free rate untaxed, and loan interest is never deductible. If yours is taxed, enter the after-tax rate.
  • Risk and access to cash. The kept cash is assumed safe and earning a fixed rate. Keeping a buffer for an emergency has a value the tool does not count.
  • A rate that floats is three paths, not a forecast. The tables read the middle. Your loan could follow any path inside the band, or outside it.
  • Penalties and promotions. No late fees, early repayment, break costs, or deferred interest charged back when a 0% promotion ends. Only the fees you enter.
  • Different end dates. Each offer is scored in the money of its own end date. Offers of different lengths compare more fairly with Show in today's money on, and that reading uses inflation, not the risk-free rate.
  • Cash that runs out. If the repayments drain the kept cash below zero, the shortfall is charged the risk-free rate, as if you could borrow at it. With Negative carry on a long loan, check the Investment Value line stays above zero.

When not to trust it. If the answer is within a few hundred dollars of zero, the choice of risk-free rate decides it, so test a point either side. If you would invest the kept cash in something risky, the tool's answer is the safe case only. And if the loan has terms you could not enter, such as a promotion that ends, read the contract, not the chart.

Ready to compare your own?

Open the tool