Compound Interest • Topic 3 of 3

Half-Yearly and Quarterly Compounding; Appreciation and Depreciation

What Happens When Compounding Period Changes?

Interest can be compounded more frequently than once per year: half-yearly (2 times per year), quarterly (4 times per year), monthly (12 times per year), or even daily.

Modified Formulas:

Compounding PeriodRate per periodNumber of periodsFormula
**Half-Yearly**r/2 %2n half-yearsA = P(1 + r/200)²ⁿ
**Quarterly**r/4 %4n quartersA = P(1 + r/400)⁴ⁿ
**Monthly**r/12 %12n monthsA = P(1 + r/1200)¹²ⁿ

More frequent compounding = More interest!

Appreciation (Growth):

When the value of an asset increases over time (property value, investments, collectibles).

Depreciation (Decay):

When the value of an asset decreases over time (cars, electronics, machinery).

Formulas for Appreciation and Depreciation:

TypeFormulaExample
**Depreciation**A = P(1 - r/100)ⁿCar value decreasing

Note: For depreciation, we use minus instead of plus in the formula.

Applications — Growth & DepreciationPopulation GrowthP_t = P_0(1 + r/100)ᵗCity with 100,000 people, 5% growth/yrAfter 3 yrs: 100000×(1.05)³ = 115,763DepreciationV_t = V_0(1 - r/100)ᵗCar worth ₹5,00,000 depreciates at 10%/yrAfter 2 yrs: 500000×(0.9)² = ₹4,05,000Growth uses (1 + r/100); Depreciation uses (1 - r/100)Key: identify whether value is increasing or decreasing
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Worked Example

Solve a standard problem on Half-Yearly and Quarterly Compounding; Appreciation and Depreciation.

Solution

Apply the formula/method shown in the concept section above.

Key Points

  • Understand the definition and properties of Half-Yearly and Quarterly Compounding; Appreciation and Depreciation.
  • Study the worked examples and practice similar problems.
  • Always verify your answer using the original conditions.
Tap an option to check your answer0 / 4
Q1.For half-yearly compounding, the rate is halved and the number of periods is:
Explanation: Doubled.
Q2.For quarterly compounding, divide the annual rate by:
Explanation: By $4$.
Q3.An increase in value over time is called:
Explanation: Appreciation.
Q4.A decrease in value over time is called:
Explanation: Depreciation.