## How to calculate duration (period) of a deposit, borrowing or lending, in order to collect or pay a certain simple flat rate interest by the principal (initial starting amount of money), simple flat interest rate and additional transaction fees (withdrawal, payment in advance, etc.).

#### Annual simple flat rate interest formula:

#### I = P × p% × n

- I = n years simple flat rate interest charged
- P = 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 of the duration of a deposit, borrowing or lending, applied to the principal - initial starting amount of money lent, deposited or borrowed - in order to earn a simple flat rate interest:

#### n = I ÷ (P × p%)

### Examples of how to calculate the duration of a deposit, borrowing or lending, for earning a due simple flat rate interest:

- 1) For how many n years a bank account should be open if the initial starting amount of money that has to be lent, deposited or borrowed, the principal, P = 20,000 units produced a simple flat rate interest (collected or paid) D = 3,500 units with an annual simple flat interest rate of p% = 3.5%?

Answer:

n = I ÷ (P × p%) = 3,500 ÷ (20,000 × 3.5%) = 3,500 ÷ (20,000 ×^{3.5}/_{100}) = (100 × 3,500) ÷ (20,000 × 3.5) = 350,000 ÷ 70,000 = 35 ÷ 7 = 5 years; - 2) For how many n years a bank account should be open if the initial starting amount of money that has to be lent, deposited or borrowed, the principal, P = 5,000 units produced a simple flat rate interest (collected or paid) D = 300 units with an annual simple flat interest rate of p% = 2%?

Answer:

n = I ÷ (P × p%) = 300 ÷ (5,000 × 2%) = 300 ÷ (5,000 ×^{2}/_{100}) = (100 × 300) ÷ (5,000 × 2) = 30,000 ÷ 10,000 = 3 years;

### Duration (period) of a simple flat interest rate investment formula calculated for a period of n years:

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

### Duration (period) of a simple flat interest rate investment formula calculated for a period of m months:

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

### Duration (period) of a simple flat interest rate investment formula calculated for a period of d days:

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

### More examples on how the duration of a deposit, borrowing or lending for earning a certain simple flat rate interest formula works:

- 1) Calculate the duration (period), m, in months, of a banking deposit account with an initial starting amount (principal) P = 400 units that would generate a simple flat rate interest I = 6.67 units with a simple flat interest rate p% = 4.5%.

Answer:

m = (12 × I) ÷ (P × p%) = (12 × 6.67) ÷ (400 × 4.5%) = (12 × 6.67) ÷ (400 ×^{4.5}/_{100}) = (100 × 12 × 6.67) ÷ (400 × 4.5) = (3 × 6.67) ÷ 4.5 = 5 months; - 2) Calculate the duration (period), m, in months, of a banking deposit account with an initial starting amount (principal) P = 400 units that would generate a simple flat rate interest I = 7.5 units with a simple flat interest rate p% = 4.5%.

Answer:

m = (12 × I) ÷ (P × p%) = (12 × 7.5) ÷ (400 × 4.5%) = (12 × 7.5) ÷ (400 ×^{4.5}/_{100}) = (100 × 12 × 7.5) ÷ (400 × 4.5) = (3 × 7.5) ÷ 4.5 = 22.5 ÷ 4.5 = 5 months.