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• Elias Zeekeh, MBA, CPA, CMA

# Demystifying Interest Rates – 4 Fundamental Concepts

Understanding interest rates is a fundamental part of personal finance whether you’re getting a loan or investing. Below are four key concepts:

Compound Interest Vs Simple Interest

The difference between simple and compound interest is that simple interest is calculated only on the principal amount, while compound interest calculates interest upon interest. So for example, say you invested \$10,000 at 10% over a 3-year period. Below is the difference in returns between simple and compound interest:

Simple Interest

Initial Investment - \$10,000

Y1 Savings Balance - \$11,000

Y2 Savings Balance - \$12,000

Y3 Savings Balance - \$13,000

CAGR: 8.37%

Annual Compound Interest

Initial Investment - \$10,000

Y1 Savings Balance - \$11,000

Y2 Savings Balance - \$12,100

Y3 Savings Balance - \$13,310

CAGR: 10.00%

There is a significant difference in the returns under the two scenarios and the difference grows exponentially over longer time periods.

Nominal Interest Rate Vs Effective Interest Rates

Does a ten percent compound interest loan actually mean that the interest rate is ten percent? The answer is maybe because it depends on what the compounding period is.The more frequent the compounding periods the higher the effective interest rate. For example, say you borrowed \$2,000 over a 3-year period at a nominal interest rate of 12%. Below is the effective interest rate under annual, semi-annual, and monthly compounding.

Compounded Annually

Initial Loan:\$2,000.00

Y1 Amount Owing: \$2,240.00

Y2 Amount Owing: \$2,508.80

Y3 Amount Owing: \$2,809.86

Effective Interest Rate: 12.00%

Compounded Semi-Annual

Initial Loan: \$2,000.00

Y1 Amount Owing: \$2,247.20

Y2 Amount Owing: \$2,524.95

Y3 Amount Owing: \$2,837.04

Effective Interest Rate: 12.36%

Compounded Monthly

Initial Loan: \$2,000.00

Y1 Amount Owing: \$2,253.65

Y2 Amount Owing: \$2,539.47

Y3 Amount Owing: \$2,861.54

Effective Interest Rate: 12.68%

Time Value of Money

Time value of money states that a dollar today is worth more than a dollar tomorrow. The rationale for this rule is that money is not “free” and has a cost in terms of interest payable. For example, if you’ll be receiving \$10,000 3-years from now and the current risk-free rate is 5% then the present value of the \$10,000 is \$8,638. Whether you’re borrowing or investing take into consideration the timing of when cash changes hands.

The Rule of 72

This is a quick way calculate how long it will take your money to double at a given an interest rate. For Example, if the effective interest rate is 6%; divide 72 by 6 and this will give you 12. This means it will take 12 years for your money to double. If your interest rate went to 8% then it would take 9 years for your money to double. Remember for retirement planning you should be working out an interest rate after fees and after taxes, this can vary significantly between investment vehicles.

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