Simple Interest * Suppoe that an investor lends you money and at the agreed date you must repay the money together with the fee charged for the use of the money, known as the interest * Interest is income from the money (capital) invested. * The capital originally invested is called the princible while the sum of the princible and the interest is called the future value. * Most interest transactions are described by the rate of interest, which is the ratio of the interest earned in one time unit to the principal. * Using the method of simple interest, the interest due t be paid at the end of the loan is based on the original principal, the term of the loan and the stated rate of interest * For these calculation the following notation is used * P= principal * I= the total simple interest * S= the future value, or maturity value of P * R= the rate of interest per period (normally per annum) * T= the time in periods (normally years)

* Simple interest is then calculated by this formula
I = Prt

* From the definition of the amount s we have:
S= P + I * Then by subbing I = PRT we obtain s interms of P,r,t
S= p + Prt
S= P(1 + rt) * The factor (1 + rt) in formula is called the simple interest factor and the process of calculating S from P by formula 2 is called the accumulation at simple interest

* We can also express P in terms of S,r and t and obtain

* When we calculate P from S, we call P the present value (PV) or the discounted value of S. * The factor (1+rt)-1 is called the present value discounted factor at simple interest * The time T must be in years when an annual interest rate is used. In these cases when the time is given in months, then: T = number of months/12

* And, when the time is given in days, then:

T = number of days/ 365

Note, we always use 365 days in a year.

Examples 1. Find the simple interest on a 90 day loan of $500 at 8.5% p.a.

2. A couple borrows 10,000. The interest rate is 1% per month and the paymet is $210. How much of the fist payment goes to interest and how much to reduce the loan?

3. A loan shark made a loan of $100 to be repaid with $120 at the end of one moth. What was the annual rate of simple interest?

4. Sixty days after borrowing money a person pays back exactly $200. How much was borrowed if the payment of $200 includes the principal and simple interest at 9% p.a.?

5. How long will it take $3000 to earn $60 interest at 6% p.a.?

The time between dates
Its important to know the exact amount of days in simple interest calculation
For this purpose we include the day the money is lent (or deposited) but exclude the day the money is repaid (or withdrawn)

Interest paid on bank balances
Many accounts with banks, building societies and credit unions earn simple interes bosed on the minimum monthly balance in the account each month. This means that a desposit and subsequent withdrawal of a sum of money within the same month will not generate any interest, as the interest calculationsuses the minimum monthly balance

Example
Minimum mothly balances are Month | Minimum balance | January | 200 | Feb. | 200 | March | 500 | April | 300 | May | 300 | June | 300 | July | 600 | August | 600 | September | 600 | October | 400 | November | 400 | December | 400 |

I = 4800 x 0.04 x 1/12
= $16

Present value
Oresent value using simple interest