# The Importance Of Interest Rates And Their Calculations (Spreadsheet).

Interest rates are important in financial decision making because they affect the value of money. By extension, they are important considerations in the valuation of financial assets, which cash is one of them.

The following tools are used to determine interest and how it affects the total amount of deferred payment due (examples of such deferred payments include hire purchase, loans and other debt financing options}.

1. Simple Interest:

Simple interest is the method of calculating interest on loan. It is quick and easy.

The formula is given as:

Amount of simple interest (SI) = Amount due or Principal (P) x Interest rate (R) x Time (T).

Example;

An interest on a debt of \$500 to be repaid after 90 days is to be charged at 15 percent per annum. The simple interest can be calculated as:

SI = \$500 x (15/100) x (90/365) = \$18.50 (use the attached spreadsheet as a guide for more calculations).

The worth of an investment can be determined at simple interest. For example, if \$5000 is invested at 10 per cent interest rate, the worth of the investment after ten years could be calculated as follows;

Using the formula; Vn = P + PRT/100,
Where Vn is the future value of the investment,
P is the principal of the investment,
R is the interest rate payable
T is the time in years.

Vn = \$5000 + (\$5000 x 10 x 10)/100 = \$10,000.

Simple interest rate doesn’t always represent actual rate charged, especially in hire purchase transaction.

For instance, a rate of 15 per cent is charged on a debt of \$500 for a year, but \$200 is repaid after four months, the ‘real’ rate is calculated by using the Annual Percentage Rate (APR).

The interest rate to be repaid is 15% of \$500 = \$75 – A,

The amount due is \$500 for 4/12 = \$167 – B,

(\$500 – \$200 = \$300) \$300 for 4/12 = \$100 – C,

The equivalent due for a year = \$267 – D (B + C)

The ‘real’ rate of interest (APR) = A/D = 75/267 = 28.1%.(use attached spreadsheet for further calculations).

2. Compound Interest:

Compound interest is used to calculate interest when interest due is more than one year. The interest charged for each year is calculated on the basis of the outstanding amount at the beginning of the year.

The outstanding amount includes interest of all previous years.

The formula for calculating the final value (amount) of an investment, where the interest is compounded is given as;

Vn = P x (1 + r)n

Where Vn is the final value (amount),
P is the principal (amount) invested,
R is the compound rate of interest.

The worth \$5000 in the example above can calculated at compound interest as follows;

The interest rate is still 10 per cent and the time is still ten years.

Vn = \$5000 x (1 + 10/100)10 = \$12,969.

Where the interest is compounded more than once a year, the formula is;

Vn = P x ( 1 + r/m)mn

Where m is the number of times interest is compounded per year and,
n is the term of maturity.

3. Present Value.

The present value; the worth of a future cash flow in terms of today’s money can be calculated using same variables as those of the compound interest formula.

Since present value is the reciprocal of compound interest rate, the present value formula is written as’

Amount (principal) invested (P) = Final Value (Vn)/(1 + r)n

Where r = the discount rate.
That is the rate at which a future cash flow is discounted to arrive at the present value