## Simple flat rate interest.

### Interest

- When someone lends money to someone else, the borrower usually pays a fee to the lender. So the due interest is a sum paid or charged for the use of money or for borrowing money.
**The interest**depends on: 1) the period of the loan 2) the amount of money lent or borrowed (called principal) and 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. 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.

### Annual simple flat interest rate

- The simple annual interest rate, or the percentage of the principal charged as interest for a period of one year, shows us that for an amount of 100 units (ex: Dollar, Euro, Yen, Pound, Franc), in a year, the interest is calculated as a percentage p% of the principal: I = p% × 100 units.
- A deposit of S units generates a one year simple interest of: I = S × p% units, and in n years, the same deposit of S units generates an interest of: I = S × p% × n units.

### Annual simple flat rate interest formula:

#### I = S × p% × n

- I = n years simple flat rate interest charged
- S = initial amount (principal)
- p% = annual simple flat interest rate (percentage of the principal charged as interest)
- n = number of years of the lending or borrowing the money

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

- 1) What interest, I, generates in n = 5 years a principal of S = 20,000 units if the annual simple flat interest rate is p% = 3.5%?

Answer:

I = S × p% × n = 20,000 × 3.5% × 5 = 20,000 × 3.5 ÷ 100 × 5 = 1,000 × 3.5 = 3,500 units - 2) What is the simple flat interest rate, p%, if a principal of S = 12,000 units is charged a n = 6 years interest of I = 2,880 units?

Answer:

I = S × p% × n =>

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

### Annual simple flat rate interest formula calculated for a period of n years:

- Interest, I = S × p% × n
- Principal, S = I ÷ (p% × n)
- Interest rate, p% = I ÷ (S × n)
- Number of years (period): n = I ÷ (S × p%)

### Annual simple flat rate interest formula calculated for a period of m months:

- Interest, I = (S × p% × m) ÷ 12
- Principal, S = (12 × I) ÷ (p% × m)
- Interest rate, p% = (12 × I) ÷ (S × m)
- Number of months of the period, m = (12 × I) ÷ (S × p%)

### Annual simple flat rate interest formula calculated for a period of d days:

- Interest, I = (S × p% × d) ÷ 365
- Principal, S = (365 × I) ÷ (p% × d)
- Simple flat interest rate, p% = (365 × I) ÷ (S × d)
- Number of days of the period, d = (365 × I) ÷ (S × p%)

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

- 1) Calculate the due interest on a principal of S = 400 units in m = 5 months, with a simple flat interest rate of p% = 4%.

Answer:

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

Answer:

I = (S × p% × m) ÷ 12 = (400 × 4.5% × 5) ÷ 12 = (400 × 4.5 ÷ 100 × 5) ÷ 12 = 18 × 5 ÷ 12 = 15 ÷ 2 = 7.5 units.