Math Without an Operator

Math Without an Operator

The CFO wants three numbers Business Central will not give her out of the box: what a loan costs per month, what a nominal interest rate really amounts to over a year, and how fast a portfolio has actually grown. Every one of these formulas raises a number to a power — and when you reach for ^ or **, the AL compiler politely informs you that no such operator exists. Your job is to build the small finance codeunit anyway.

Requirements

Create a codeunit named "Compound Interest" with three public procedures:

procedure MonthlyPayment(Principal: Decimal; AnnualRatePct: Decimal; Months: Integer): Decimal
procedure EffectiveAnnualRate(NominalRatePct: Decimal; CompoundingsPerYear: Integer): Decimal
procedure CAGR(StartValue: Decimal; EndValue: Decimal; Years: Decimal): Decimal

Pick object IDs in the range 50100–50199, and reference other objects by name, never by ID.

MonthlyPayment — the annuity formula

• The monthly rate is r = AnnualRatePct ÷ 100 ÷ 12, so MonthlyPayment(200000, 6, 360) uses r = 0.005.
• The payment is Principal × r × (1 + r)^Months ÷ ((1 + r)^Months − 1). For the 200,000 loan at 6% over 360 months that is 1,199.10 a month.
• Zero-rate special case: when AnnualRatePct is 0, the formula above divides by zero — an interest-free loan simply splits the principal evenly, so return Principal ÷ Months.
• The tests only pass Principal > 0, AnnualRatePct ≥ 0 and Months ≥ 1; you do not need to validate these inputs.

EffectiveAnnualRate — what a nominal rate compounds to

• A nominal annual rate of NominalRatePct, compounded CompoundingsPerYear times a year, really yields ((1 + NominalRatePct ÷ 100 ÷ CompoundingsPerYear)^CompoundingsPerYear − 1) × 100 percent per year.
• Example: 12% compounded monthly is EffectiveAnnualRate(12, 12) = 12.682503…% — return the percentage, not the fraction.
• With annual compounding (CompoundingsPerYear = 1) the effective rate equals the nominal rate, and a 0% nominal rate yields 0 — both fall out of the formula with no special casing.
• The tests only pass NominalRatePct ≥ 0 and CompoundingsPerYear ≥ 1.

CAGR — compound annual growth rate

• A value that grew from StartValue to EndValue over Years years grew at ((EndValue ÷ StartValue)^(1 ÷ Years) − 1) × 100 percent per year.
• Years is a Decimal and may be fractional: 2.5 years is a valid holding period, and the exponent 1 ÷ Years is then not a whole number.
• When EndValue is smaller than StartValue the result is negative, and when they are equal it is 0.
• If StartValue, EndValue or Years is zero or negative, the math is meaningless — raise an error with a message that contains the word positive.

Return the raw computed values — do not round. Payments are graded within ±0.01, so rounding a payment to the cent happens to survive, but rounding a rate to two decimals will fail the ±0.0001 tolerance on the rate procedures.

What the tests check

Fixed textbook cases are asserted within tolerance (±0.01 on payments, ±0.0001 on percentage rates): the 200,000 mortgage above, an interest-free loan, a one-month loan (which must come out at Principal × (1 + r)), monthly versus annual compounding, a 0% nominal rate, a portfolio that doubles in ten years (7.1773…% a year), one that halves (negative CAGR), one that is flat (0), and a fractional 2.5-year holding period. CAGR must raise the promised error (message checked for positive) for a zero or negative StartValue, EndValue and Years. Finally, randomly generated loans, rates and growth histories are graded against an independent computation of the same formulas, so hardcoding the examples fails.

Learn More

• AL operators — the complete operator list; note which arithmetic operators AL does and does not have.
• Arithmetic operators — how AL converts types when Integers and Decimals mix in a formula.
• Decimal data type — range and precision of the type all three procedures return.
• Dialog.Error method — raising the validation error CAGR promises.