### Interest

- When someone lends money to someone else, the borrower usually pays a fee to the lender. So the due interest is an amount of money paid or charged for the use of money or for borrowing money.

**The interest**depends on:- 1) the period length of the loan
- 2) the amount of money lent or borrowed (called principal)
- 3) the interest rate (the percentage of the principal charged as interest).
- For example, for some bank deposits is not uncommon to pay an interest rate of 3.5% on the principal, annualy. That means that at the end of a one-year period the bank will repay not only the amount that was initially deposited, but also an additional amount, equal to the value resulting from the calculation: 3.5% × P, where P is the initial amount deposited, the principal.
- Banks are also using these temporarily owned amounts of money by introducing them back into the cash flow circuit or are granting loans (for investments, for example) on which they are again charging interest.

### The annual simple flat interest rate

- The simple annual interest rate is simply the percentage of the principal charged as an interest for a period of one year, charged at the end of the period. An interest rate of r% tells us that for an amount of 100 (Dollar, Euro, Pound, Franc, Yen, ...), in one year, an amount of (r% out of 100) is earned as interest: I = r% × 100 units.

- 1. A deposit of an amount of money units P generates a one year simple interest of:
- I = r% × P.
- 2. If the period for which the interest is calculated is two years, the interest accrued on a deposit of P money units is:
- I = r% × P + r% × P = 2 × r% × P.
- n. If the period for which the interest is calculated is n years, the interest accrued on a deposit of P money units is:
- I = r% × P + r% × P + ... + r% × P = n × r% × P.
- You can see that the amount accrued as interest, called simple interest, is added to the initial amount which earns interest, the amount borrowed or deposited, only at the end of the period of the deposit.
- Simple interest is not an interest that earns interest on interest, as is the compound interest

### Annual simple flat rate interest formula:

#### I = n × r% × P

- I = simple flat rate interest earned in a period of n years long
- P = initial amount that earns the interest (principal)
- r% = annual simple flat interest rate (percentage of the principal charged as interest)
- n = number of years of the period of the lending or borrowing the money

### Examples of how the simple flat rate interest formula works:

- 1) What is the amount of the value of the interest, I, generated in n = 5 years by a principal of P = 20,000 money units if the annual simple flat interest rate is r% = 3.5%?
- Answer:

I = n × r% × P × = 5 × 3.5% × 20,000 = 5 × 3.5 ÷ 100 × 20,000 = 1,000 × 3.5 = 3,500. - 2) What should be the simple flat interest rate, r%, if a principal of P = 12,000 money units earned a n = 6 years interest of I = 2,880?
- Answer:

I = n × r% × P =>

r% = I ÷ (P × n) = 2,880 ÷ (12,000 × 6) = 0.04 = 4%.

### Annual simple flat rate interest formula calculations, for a period length of n years:

- Interest, I = n × r% × P
- Principal, P = I ÷ (r% × n)
- Interest rate, r% = I ÷ (P × n)
- Number of years (period length, in years): n = I ÷ (P × r%)

### Annual simple flat rate interest formula calculations, for a period length of m months:

- N = Number of months in a year, N = 12.
- Interest, I = (m × r% × P) ÷ N
- Principal, P = (N × I) ÷ (r% × m)
- Interest rate, r% = (N × I) ÷ (P × m)
- Number of months of the period length, m = (N × I) ÷ (P × r%)

### Annual simple flat rate interest formula calculations, for a period length of d days:

- N = Number of days in a year, N = 360 or 365, depending on the chosen method of calculation.
- Interest, I = (d × r% × P) ÷ N
- Principal, P = (N × I) ÷ (r% × d)
- Simple flat interest rate, r% = (N × I) ÷ (P × d)
- Number of days of the period length, d = (N × I) ÷ (P × r%)

### More examples on how the simple flat rate interest formula works:

- 1) Calculate the due interest on a principal of P = 400 money units in m = 5 months, with a simple flat interest rate of r% = 4%.
- Answer:

I = (P × r% × m) ÷ 12 = (400 × 4% × 5) ÷ 12 = (400 × 4 ÷ 100 × 5) ÷ 12 = 16 × 5 ÷ 12 = 20 ÷ 3 = 6.67. - 2) Calculate the due interest earned by a principal of P = 400 money units in m = 5 months if the simple flat interest rate of r% = 4.5%.
- Answer:

I = (P × r% × m) ÷ 12 = (400 × 4.5% × 5) ÷ 12 = (400 × 4.5 ÷ 100 × 5) ÷ 12 = 18 × 5 ÷ 12 = 15 ÷ 2 = 7.5.