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PART IX — MATHEMATICAL FINANCE🔵 Intermediate

Is This Bond a Good Investment at the Current Price?

Bond Mathematics

Price, yield to maturity, duration, and convexity — the quantitative toolkit every fixed income and credit investor must master.

math financebondsYTMdurationconvexityfixed income

Live Result

$973.269881

ƒ: coupon / (1 + y)^1 + coupon / (1 + y)^2 + (c…raw: 973.270

ƒ(x)

Use variable names from the panel above (e.g. FV, r, n) — or type numbers directly: 10000 / (1 + 0.08)^10

coupon

Annual coupon payment ($)

coupon = 50

face

Face (par) value at maturity ($)

face = 1000

y% as decimal

Yield to maturity (decimal)

y = 0.06

price

Current market price of bond ($)

price = 950

duration

Modified duration (years)

duration = 4.5

delta_y% as decimal

Change in yield (decimal)

delta_y = 0.01

💡 You can also enter values directly in the formula: 10000 / (1 + 0.08)^10

⬇ Export Calculation

Exports a plain .txt file with your expression, formula, all variable values, result, and educational notes — ready to paste into any report, Word doc, Notion, or Google Docs.

The exported file includes the formula in standard mathematical notation — you can paste it directly into Excel, Google Sheets, or back into FinanceSheep.

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Learn: Bond Mathematics

PART IX — MATHEMATICAL FINANCE · Educational Guide

The Core Idea

A bond is a stream of future cash flows — coupon payments and a final principal repayment. Its price is simply the present value of those cash flows discounted at the market yield. When market yields rise, bond prices fall — this is the most important inverse relationship in fixed income and it directly affects WACC and discount rates in equity valuation.

How It Works

Price = Σ [C / (1+y)^t] + [F / (1+y)^T]. YTM is the internal rate of return — the yield making PV of cash flows equal the market price. Duration measures price sensitivity: a 1% yield rise drops price by approximately Duration%. Modified duration = Macaulay Duration / (1+y). Convexity is the second-order correction — actual price change is slightly better than duration predicts because of curvature in the price-yield relationship.

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Real-World Example: 3-year bond, $1,000 par, 5% coupon, YTM = 6%: Price = 50/1.06 + 50/1.06² + 1,050/1.06³ = 47.17 + 44.50 + 881.68 = $973.35 (trading at a discount because coupon rate 5% < market yield 6%). Current yield: $50/$973.35 = 5.14%. If modified duration = 2.83 and yield rises 1%: ΔPrice ≈ −2.83% × $973.35 = −$27.55 new price ≈ $945.80. Long duration bonds (30-year Treasuries, duration ≈ 18) are hit far harder by rising rates than short-duration bills.

Is This Bond a Good Investment at the Current Price?

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