Compound Interest and its Calculation Methods

Compound Interest:

Compound interest is calculated on the principal amount and any accrued interest (“interest on interest”), leading to accelerated financial growth.

Simple vs. Compound Interest:

Compounding Period:

The compounding period is the time interval at which interest is added to the principal. It can be annual, semi-annual, quarterly, monthly, daily, or continuous. Shorter compounding periods lead to a greater impact from compound interest.

Methods of Calculating Compound Interest:

1. Manual Calculation: Calculate interest for each compounding period and add it to the balance.

   • Example: $100 with 10% annual interest compounded quarterly.
     • Quarter 1: Interest = $100 * (10%/4) = $2.50. New balance = $102.50.
     • Quarter 2: Interest = $102.50 * (10%/4) = $2.56. New balance = $105.06.
     • Quarter 3: Interest = $105.06 * (10%/4) = $2.63. New balance = $107.69.
     • Quarter 4: Interest = $107.69 * (10%/4) = $2.69. New balance = $110.38.
     • Balance after one year: $110.38.

2. Mathematical Formula:

   FV = PV * (1 + r/n)^(nt)

   • FV = Future Value
   • PV = Present Value (Principal)
   • r = Annual interest rate❓ (decimal)
   • n = Number of times interest is compounded per year
   • t = Number of years

   Example: $1000 invested at 5% annually, compounded monthly for 10 years.

   • PV = $1000
   • r = 0.05
   • n = 12
   • t = 10

   FV = 1000 * (1 + 0.05/12)^(12*10) ≈ $1647.01

3. Financial Tables: Pre-calculated tables for FV and PV of investments with compound interest.

4. Financial Calculators and Accounting Software: Built-in functions for calculating compound interest.

Practical Applications of Compound Interest:

1. Investments: Crucial for long-term growth in stocks, bonds, and real estate.
2. Savings Accounts: Banks use compound interest to calculate interest on savings accounts.
3. Loans: Interest on loans (e.g., mortgages, car loans) is calculated using compound interest.
4. Retirement Planning: Essential for estimating savings needed to achieve financial goals.
5. Real Estate Valuation: Some valuation methods use concepts similar to compound interest.

Real Estate Valuation Methods:

1. Hoskold Method❓❓:

   • Estimates the present value of annual capital recovery income from an investment, assuming income is placed in a sinking fund at a safe rate.
   • Suitable for depleting assets❓ (e.g., mines).
   • Formula (simplified): Present Value = (Annual Return) / (Yield Rate + Sinking Fund Rate)
   • Note: Rarely used currently.

2. Inwood Method:

   • The present value of investment recovery through cash flow depends on a single discount rate.
   • Assumes the annual amount for capital recovery, with a stable annual income, is able to realize compound interest and is amortized completely.
   • More common than the Hoskold method but requires a good understanding of discount rates and financial tables.

Advice for Real Estate Appraisers:

Real estate appraisers should be knowledgeable in financial and statistical calculations, including compound interest, as these concepts are used in various aspects of real estate valuation (e.g., cash flow analysis, estimating discount rates).

Measures of Central Tendency:

Appraisers often calculate averages to determine prevailing values in a neighborhood, average rental rates, or gross rent multipliers.

1. Mean❓❓: Arithmetic average (sum of values divided by the number of values).
2. Median: Middle value in a sample.
3. Mode: Most frequent value in a sample.
4. Range: The difference between the lowest and highest number in the sample.

Example: In a sample of values: 1, 2, 3, 4, 4.

2. 8 is the Mean
   3 is the Median
   4 is the Mode
   1-4 is the Range

Standard Deviation:

A mathematical formula that measures how much prices❓ vary from the average (mean). A small standard deviation means most prices are nearly identical. The larger the standard deviation, the more the prices vary.