# Interest Rate

## Interest Rate

An interest rate is the percentage of a borrowed or invested amount that is paid to the lender or the investor as repayment.

### Properties

• The nominal interest rate is the rate determined at the conclusion of a loan or investment.
• The periodic interest rate corresponds to the real rate divided by the number of periods of calculation (monthly: 12 periods; quarterly: 4 periods; bi-annually: 2 periods; etc.)
• The real or effective interest rate is the percentage that corresponds to the total amount of interest calculated over a year divided by the initial amount of the loan or investment at the start of the year.
• The return (or rate of return) over a certain amount of time is the percentage that corresponds to the total amount of interest calculated during this interval divided by the initial amount of the investment at the start of the interval.

### Examples

• Simple interest:
A person borrows an amount of $1000 for a period of 12 months, while the lending institution’s annual loan rate is 6%, payable every month. In this case, the nominal rate is 6% and the periodic interest rate is 0.5% (6 ÷ 12 = 0.5). The person must pay$5 of interest every month (because 0.005 × 1000 = 5). After one year, the person will have paid $60 in interest, which corresponds to 6% of the initial value of the loan. In this situation, the effective rate and the nominal rate are equal. • Compound interest: A person invests$1000 for five years in an investment fund earning 12% interest, compounded every quarter (4 times in the year). In this case, the nominal rate is 12% and the periodic rate is 3% (12 ÷ 4 = 3). Because the interest is capitalized (added to the capital) each quarter, the value of the investment will be multiplied by 1.03 each period. At the end of the four periods (1 year), the investment will have a value of $1125.51 (because 1000 × 1.034 = 1125.51 ). This amount corresponds to an effective rate of 12.51%. At the end of the five-year term (20 quarters), the investment will have a value of$1806.11 (because 1000 × 1.0320 = 1806.11 ). The profit will be \$806.11 (1806.11 − 1000 = 806.11) and the return over five years will be 80.6% (because 806.11 ÷ 1000 ⁡≈ 80.6%).