## Simple flat rate interest.

### Interest

- When someone lends money to someone else, the borrower usually pays a fee to the lender. So the 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 lent or borrowed (called principal) and 3) the interest rate (the percentage of the principal charged as interest). - For example, for some bank deposits an interest rate of 3.5% on the principal is paid, 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) for which they are charging interest.

### Annual interest rate

- The annual interest rate, or the percentage of the principal charged as interest for one year, shows us that for an amount of 100 units (EUR Euro, USD Dollars), in a year, the interest is calculated as p% of the principal: I = p% * 100 units (EUR Euro, USD Dollars).
- A deposit of S units generates a one year 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 interest formula:

#### I = S * p% * n

- I = n years interest charged
- S = initial amount (principal)
- p% = annual 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 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 interest formula calculated for a period of n years:

- Interest, I = S * p% * n
- Principal, S = D / (p% * n)
- Interest rate, p% = I / (S * n)
- Number of years for the period, n = I / (S * p%)

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

- Interest, I = (S * p% * d) / 365
- Principal, S = (365 * I) / (p% * d)
- 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 interest formula works

- 1) Calculate the interest generated by a principal of S = 400 units in m = 5 months with an 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 interest generated by a principal of S = 400 units in m = 5 months with an 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.