Deferred Payment and Bond Calculator

How to work it out yourself

1. 1.Choose which end you know. Lending money and asking what comes back is the deferred case; being promised an amount and asking what to pay for it is the bond case.
2. 2.Set the compounding frequency to match the instrument. US bonds conventionally use semi-annual compounding, and using annual instead understates the yield.
3. 3.Read the multiple. It is the same number for any principal, which makes it the quickest way to compare two terms without arithmetic.

The formula

1. What one dollar grows to over the term
2. Effective annual yield(pow(factor, 1 / years) - 1) * 100
3. Owed at maturityprincipal * factor
4. Worth todaydue_amount / factor
5. Answermode_deferred * amount_due + mode_bond * present_value
6. Interest over the termmode_deferred * (amount_due - principal) + mode_bond * (due_amount - present_value)
7. Multiple of the starting amountfactor
8. Years to double at this raterate == 0 ? 0 : log(2) / log(pow(factor, 1 / years))

Source: US SEC Investor.gov — bonds and how they are priced, US Treasury — securities pricing and accrued interest

Questions people actually ask

How is this different from an instalment loan?

Nothing is repaid until maturity, so the balance never falls and interest compounds on the whole amount for the whole term. An instalment loan of the same size and rate costs far less, because every payment removes principal that would otherwise have carried interest for the rest of the term.

What is the bond mode for?

Discounting: turning a known amount due later into what it is worth now. A zero-coupon bond paying $50,000 in ten years at 6% is worth $27,919 today, and that is the price at which buying it earns exactly 6%. Pay more and you earn less than 6%.

Does this price a coupon bond?

No. This handles a single payment at maturity — a zero-coupon bond, a discount note, or a balloon. A bond paying regular coupons is the sum of many discounted payments plus the discounted face value, and each coupon needs its own term.

Why does compounding frequency matter more here?

Because there is nothing else happening. On an instalment loan the payments dominate; here the only mechanic is interest earning interest, so the frequency compounds over the entire term. Over ten years at 6%, annual compounding gives 1.791 times the principal and continuous gives 1.822.

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