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Classic

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

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

RATE AND TIME MUST BE IN THE SAME UNIT

Value acquired

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

Average Investment Rate

Average Investment Rate: The average interest rate of multiple loans

Steps:

  1. Sum all interests
  2. Replace t with T to equal the total interests
  3. Solve for T

(BONUS) Formula

T=Total Interesti=0Ci×ni100=i=0Ci×ti×nii=0Ci×ni100\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

I=2000×4.25100×1=2000×4.25×1100=85$\text{I} = 2000 \times \frac{4.25}{100} \times 1 = \frac{2000 \times 4.25 \times 1}{100} = 85\$

Interest 2

I=1500×0.3100×8=1500×0.3×8100=36$\text{I} = 1500 \times \frac{0.3}{100} \times 8 = \frac{1500 \times 0.3 \times 8}{100} = 36\$

Interest 3

I=750×5.5100×120360=750×5.5×120100×360=750×5.5×12036000=13.75$\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\$

Total Interest

I=85+36+13.75=134.75$\text{I} = 85 + 36 + 13.75 = 134.75\$

Step 2: Replace t with T

Total Interest=2000×T100+1500×T×8100×12+750×T×120100×360=2000×T100+1500×T×81200+750×T×12036000\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}

We divide the second by 12 because the rate t is given in months while we want it in years.

Step 3: Solve for T

134.75=2000×T100+1500×T×81200+750×T×12036000134.75 = \frac{2000 \times \text{T}}{100} + \frac{1500 \times \text{T} \times 8}{1200} + \frac{750 \times \text{T} \times 120}{36000}

134.75=20×T+10×T+2.5×T134.75 = 20 \times \text{T} + 10 \times \text{T} + 2.5 \times \text{T}

134.75=32.5×T134.75 = 32.5 \times \text{T}

T=134.7532.5=4.14%\text{T} = \frac{134.75}{32.5} = 4.14\%

Formula

T=134,752000×1100+1500×812×100+750×120360×100 \text{T} = \frac{134,75}{\frac{2000 \times 1}{100}+\frac{1500\times8}{12\times100}+\frac{750\times120}{360\times100}}

=134,752000×1100+1500150+12048= \frac{134,75}{\frac{2000 \times 1}{100}+\frac{1500}{150}+\frac{120}{48}}

=134,7520+10+2,5= \frac{134,75}{20+10+2,5}

=134,7532,5= \frac{134,75}{32,5}

=4,14%= 4,14\%

Proportional Periodic Rate

Proportional Periodic Rate=Annual rate×DurationDuration of Year\text{Proportional Periodic Rate} = \frac{\text{Annual rate} \times \text{Duration}}{\text{Duration of Year}}

  • Annual rate: Rate of interest per year
  • Duration: Duration of loan
  • Duration of Year: Duration of a year (360 days, 360 days, 12 months, etc.)

Two proportional rate with same capital & same period should give same interest.

When?

Post-counted Interest

Post Counted Interest Image Post Counted Interest Image

Pre-counted Interest

Pre Counted Interest Image Pre Counted Interest Image

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