Simple Interest
Interest: Income from sum of money lent
Depends on:
- Capital (amount of money lent, "C")
- Rate (interest rate, "t")
- Time (duration of loan, "n")
- 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
Interest=Capital×Rate×Time
RATE AND TIME MUST BE IN THE SAME UNIT
Value Acquired=Capital+Interest
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
T=∑i=0100Ci×niTotal Interest=∑i=0100Ci×ni∑i=0Ci×ti×ni
DON'T FORGET TO CONVERT THE RATE TO THE SAME UNIT
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
I=2000×1004.25×1=1002000×4.25×1=85$
I=1500×1000.3×8=1001500×0.3×8=36$
I=750×1005.5×360120=100×360750×5.5×120=36000750×5.5×120=13.75$
I=85+36+13.75=134.75$
Total Interest=1002000×T+100×121500×T×8+100×360750×T×120=1002000×T+12001500×T×8+36000750×T×120
We divide the second by 12 because the rate t
is given in months while we want it in years.
134.75=1002000×T+12001500×T×8+36000750×T×120
134.75=20×T+10×T+2.5×T
134.75=32.5×T
T=32.5134.75=4.14%
T=1002000×1+12×1001500×8+360×100750×120134,75
=1002000×1+1501500+48120134,75
=20+10+2,5134,75
=32,5134,75
=4,14%
Proportional Periodic Rate=Duration of YearAnnual rate×Duration
- 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.

