## How to calculate the principal - initial amount of money lent, deposited or borrowed in order to collect or pay a simple flat rate due interest by the interest rate, duration and additional fees (transaction fee as withdrawal, payment in advance, etc.).

#### Annual simple flat rate interest calculation formula:

#### I = S × p% × n

- I = n years simple 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
### Formula for the principal - initial amount of money lent, deposited or borrowed in order to produce a simple flat annual rate:

#### S = I ÷ (p% × n)

### Examples of how to calculate the initial amount, the principal, to earn a certain simple flat rate interest:

- 1) What is the principal that has to be lent, deposited or borrowed for a period of n = 5 years if the simple flat rate interest collected or paid D = 3,500 units, for an annual simple flat interest rate (percentage) p% = 3.5%?

Answer:

S = I ÷ (p% × n) = 3,500 ÷ (3.5% × 5) = 3,500 ÷ (3.5/100 × 5) = (3,500 × 100) ÷ (3.5 × 5) = 350,000 ÷ 17.5 = 20,000 units - 2) What is the principal that has to be lent, deposited or borrowed for a period of n = 3 years if the simple flat rate interest collected or paid D = 300 units, for an annual simple flat interest rate p% = 2%?

Answer:

S = I ÷ (p% × n) = 300 ÷ (2% × 3) = 300 ÷ (2/100 × 3) = (300 × 100) ÷ (2 × 3) = 30,000 ÷ 6 = 5,000 units

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

- Principal, S = I ÷ (p% × n)
- Simple interest, I = S × p% × n
- Simple flat interest rate, p% = I ÷ (S × n)
- Number of years for the period of the deposit, lending or borrowing, n = I ÷ (S × p%)

### The principal formula for earning an annual simple flat rate interest calculated for a period of m months:

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

### The principal formula for earning an annual simple flat rate interest calculated for a period of d days:

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

### More examples of how to calculate the principal for earning a simple flat rate interest:

- 1) Calculate the initial amount S that would generate a simple flat rate interest I = 6.67 units in m = 5 months with a simple interest rate of p% = 4%.

Answer:

S = (12 × I) ÷ (p% × m) = (12 × 6.67) ÷ (4% × 5) = (12 × 6.67) ÷ (4/100 × 5) = (100 × 12 × 6.67) ÷ (4 × 5) = (100 × 12 × 6.67) ÷ 20 = 5 × 12 × 6.67 = 400.2 ≈ 400 units - 2) Calculate the initial amount that would earn a simple flat rate interest I = 7.5 units in m = 5 months with a simple flat interest rate of p% = 4.5%.

Answer:

S = (12 × I) ÷ (p% × m) = (12 × 7.5) ÷ (4.5% × 5) = (100 × 12 × 7.5) ÷ (4.5 × 5) = (100 × 12 × 7.5) ÷ 22.5 = 9,000 ÷ 22.5 = 400 units.