An interest rate is the cost of borrowing or the gain from lending, usually expressed as an annual percentage rate; it is generally calculated by dividing the interest amount by the principal amount.

Interest rates change with factors such as supply and demand for money, inflation, and central bank policies.

- Interest is the income earned from lending or investing a sum of money, i.e., the capital or principal.
- The interest rate will be defined as the amount of interest earned for the period concerned per unit of currency invested at the beginning. It is conventionally quoted as a percentage rate per annum.

The ability to work with interest calculations is of fundamental importance to investment performance and anyone in finance. First, we will look at market conventions for quoting interest and how it is computed during various investment periods.

### Market Conventions

#### Basis points

Many interest rates are quoted to 4 decimal places, e.g., 0.0750 for 7.50%; The last decimal place is called a basis point, i.e.one-hundredth of, one-hundred. If the interest rate rises from 0.0750 to 0.0754, we would say that the interest rate has increased by 4 basis points or from 0.0750 to 0.0850, by 100 basis points. The term ‘basis points’ is often abbreviated to bp.

#### Example: Basis Points

If an interest amount of Rs 15,000 is payable at the end of a year on an investment or loan of Rs 100,000, then the annual interest rate is 15,000/100,000 = 0.1500 expressed as a decimal, or 100% x 0.1500 = 15.00%.

### Quoting Interest Rates

This section considers how the rate (reflecting a return on an investment or a cost of borrowing) can be quoted on different instruments and in other markets.

The fact that different instruments and markets quote returns differently is a problem because it makes comparing these instruments difficult. For comparisons to be made, the interest rate must be converted to an everyday basis across all devices considered.

The three things needed to evaluate an interest rate are:

- The rate itself is commonly quoted as a rate per annum (i.e. ‘annualized’ rate)
- How often is this interest credited, e.g., daily, monthly, semi-annually, annually?

Whether interest is simple or compounded.

### Simple interest rates

Markets usually quote nominal interest rates for investment periods on a simple annualized basis.

Simple interest is where the total interest for the given period is levied only on the original principal amount. In this case, no interest is earned on the interest accumulated in previous periods. The term annualized means that the rate is quoted as if for a whole year.

#### The formula of Simple Interest

FV = PV x [1+ R * (days / year)]

Where,

- PV = Present Value (principal invested)
- FV = Future Value (final or accumulated value of principal plus interest)
- R = annual simple interest rate
- days = number of days the investment is held
- year = number of days in a conventional year (360 or 365)

#### Example: Simple Interest

A short-term deposit of Rs 100,000 is made for 60 days at an annual simple interest rate of 6%. The future value 60 days hence of principal plus simple interest would be Rs 100,000 x (1+0.06 x 60/360) = Rs 101,000.

### Periodic Interest Rates

Often interest is credited (or charged) more often than once a year. The interval of time between successive interest payments is called a period. The interest that is paid each period is called periodic interest. The periodic rate is always a simple interest rate

#### The formula gives the periodic interest rate:

r = R x (days/year)

**Where:**

- r = periodic interest rate
- R = annual simple interest rate
- days = the number of actual days in the period
- year = the number of days in a conventional year (360 or 365)

A simple annualized interest rate can be derived from a periodic rate:

R = r x (year/period)

Periods could be days, weeks, months, quarters, or a half year.

#### Example: Periodic Interest Rate

A money market instrument is quoted at 10%, paying interest quarterly. The periodic interest rate per quarter would be 2.5% (i.e., 10% /4)

### Compound Interest Rates

Compounding is an arrangement where ‘interest is paid on the interest’ and interest on the original principal. Consequently, compound interest for multiple compounding periods is higher than simple interest.

#### Compound Interest Formula

FV = PV x (1 + r)^n

**Where:**

n = number of compounding periods,

r = periodic interest rate

#### Example: Compound Interest

A deposit of Rs 100,000 is made for 2½ years at an annual interest rate of 6%. Interest is paid annually and reinvested. Estimate the future value 2 ½ years hence of principal plus compound interest:

Rs 100,000 x (1+0.06)^2.5 = Rs 115,682

In this example, the compounding period is a year, with 2.5 compounding periods.

(The annual interest rate is used here as an approximate periodic rate, interest on an actual deposit would be calculated based on the number of days in 2.5 years and the number of days in a conventional year for USD, which is 360.)

### Effective Annual Rates

Comparing investment instruments, the Effective Annual Rate of interest (EAR) is used. EAR is the annual interest rate earned after adjusting for the effects of compounding. EAR assumes that interest is compounded at the end of each interest period. Therefore, the EAR is calculated as a periodic interest rate with interest paid yearly

WWhileEAR is not a market quotation method, all instruments have an effective annual rate, regardless of the frequency with which interest is calculated and charged or credited; thus, EAR can be used to compare the returns of different nominal rates with varying periods of compounding

#### Effective annual rate EAR = (1+ r)^ (year/days)

**Where:**

- r = periodic interest rate,
- days = number of days in the period,
- year = number of days in a standard year (365 days),
- EAR is always calculated on a 365-day basis regardless of the market or currency of the cashflows.

#### Example: Effective Annual Rate (EAR)

A credit card has an amount outstanding with a periodic interest of 0.3% charged weekly. The EAR would be 16.91%, i.e. [ 1+0.003) ^ (365/7)]

### Nominal Interest Rates

As stated earlier, markets usually quote nominal interest rates for investment periods on a simple annualized basis. A nominal rate will always include inflation and be annualized. When evaluating investments across different currencies or countries, it is helpful to know the “real” return, i.e., the return excluding inflation. Wherever possible, the comparison should be made in terms of the EAR.

#### (1+Real Rate) = (1+Nominal Rate) / (1+ Inflation Rate)

#### Example: Nominal Interest Rate

If an instrument yields 12% nominal, including inflation, and inflation is 5%, the ‘real’ rate on this instrument would be

1+Real Rate = (1+ 12%) / (1+5%)

Real Rate= 1.067

### Bottomline: Interest Rate Affects Investment Decision Making

Interest rate affects our daily life. It’s not just investments; the general economic environment is also affected by interest rates. We often see rising inflation and actions taken by the central bank to tame inflation. It’s the interest rate that the central bank tries to adjust to control inflation.

If an economy overheats and inflation breaches a threshold point, the central bank usually increases the interest rate to control inflation. This is a ripple effect; investments in fixed income products offered by banks, corporations, and NBFCs grow. It also brings foreign investment into the country as foreign investments find better investment opportunities in a country with a high-interest rate.

A low-interest rate diverts investments to the stock market and other asset classes, as fixed-income securities lose their attractiveness in the short term. Conservative investors and those aged 50 years and above prefer a high-interest rate regime, particularly retirees.