Simple Interest

Basics

Interest: Income from sum of money lent

Depends on:

Capital (amount of money lent, "C")
Rate (interest rate, "t")
Time (duration of loan, "n")

Duration Rules

1 Year = 12 months = 24 fortnights = 52 weeks = 360 days
February: 28 days
All months have 30 days
Fortnight: From 1st of the month to 15th of the month or 16th of the month to the end of the month

Formula

$\text{Interest} = \text{Capital} \times \text{Rate} \times \text{Time}$

RATE AND TIME MUST BE IN THE SAME UNIT

Value acquired

$\text{Value Acquired} = \text{Capital} + \text{Interest}$

Average Investment Rate

Average Investment Rate: The average interest rate of multiple loans

Steps:

Sum all interests
Replace t with T to equal the total interests
Solve for T

(BONUS) Formula

$\text{T} = \frac{\text{Total Interest}}{\sum_{i=0}^{}\frac{C_i\times n_i}{100}} = \frac{\sum_{i=0}^{}C_i\times t_i \times n_i}{\sum_{i=0}^{}\frac{C_i\times n_i}{100}}$

DON'T FORGET TO CONVERT THE RATE TO THE SAME UNIT

Example

Capital: 2000$
Rate: 4.25%/year
Duration: 1 year

Capital: 1,500$
Rate: 0,3%/month
Duration: 8 months

Capital: 750$
Rate: 5,5%/year
Duration: 120 days

Step 1: Sum all interests

Interest 1

$\text{I} = 2000 \times \frac{4.25}{100} \times 1 = \frac{2000 \times 4.25 \times 1}{100} = 85\$$

Interest 2

$\text{I} = 1500 \times \frac{0.3}{100} \times 8 = \frac{1500 \times 0.3 \times 8}{100} = 36\$$

Interest 3

$\text{I} = 750 \times \frac{5.5}{100} \times \frac{120}{360} = \frac{750 \times 5.5 \times 120}{100 \times 360} = \frac{750 \times 5.5 \times 120}{36000} = 13.75\$$

$\text{Total Interest} = \frac{2000 \times \text{T}}{100} + \frac{1500 \times \text{T} \times 8}{100 \times 12} + \frac{750 \times \text{T} \times 120}{100 \times 360} \\ = \frac{2000 \times \text{T}}{100} + \frac{1500 \times \text{T} \times 8}{1200} + \frac{750 \times \text{T} \times 120}{36000}$