Interest is classified into two types. They are:
Simple interest
Compound interest
Simple interest: Simple interest is money we can earn by primarily investing some amount in bank or somewhere else (the principal). The percentage (the interest) of the principal amount is added to the principal, simple interest will increase our initial investments grow.
Compound interest: The difference between the original principal and the amount at the end of the last time period is known as the compound interest on the original principal period for that.
The important difference between compound and simple interest is that simple interest is paid only on the principal, whereas compound interest is paid on both the principal and the accumulated interest.
Interest formula
Simple interest formula:
The formula used for calculating the simple interest is
SI = `(PNR)/100`
Where,
P is the Principal,
N is the time period,
R is the rate of interest.
Compound interest formula:
The formula used for calculating the compound interest is
A = P (1 + `r / 100` )n
Where,
P is the Principal
R is the rate of interest
N is the number of years.
Solved Examples
Pro 1: Find the simple interest on an amount of $500 for one year at the rate of 6% per annum.
Sol: The formula is SI = PNR / 100
Principal (P) = $500
Rate of interest(r) = 6 % per annum
N= Interest on 100 dollar for 1 year = $6
Interest on 500 dollar for 1 year =6 / 100 × 500 = $30
Therefore the interest is $30.
Pro 2: Find the amount of and compound interest on $6000 for 3 years at 3% per annum.
Sol: Let p1, p2, p3… represents the principal for the first year, second year, third year and so on. Also let I1, I2, I3… represent interest for the first year, second year, third year and so on.
Understanding Definition of Compound Interest is always challenging for me but thanks to all math help websites to help me out.
The formula is A = P (1 +` r / 100` )n
C.I. = A – P
P = $6000, r = 3%, n = 3 years
A = P (1 + `r / 100` )` ^n ` = 6000 (1 + `3 / 100` )3
= 6000 (`103 / 100)` 3
= 6000 * 103 * 103 * 103 / 100 * 100 * 100
= 6556.36
Therefore
A = $6556.36
P = $6000
C. I. = A – P = 6556.36 – 6000 = 556.36
C. I. = $556.36
Pro 3: Find the amount and compound interest on 5000 dollars for 1.5 years at 8%per annum. Interest being is added to the principal every half year.
Sol: P = 5000dollars, n= 3 (three half years), r = `8/ 2` = 4%
A = P (1+`r / 100)` n = 5000 (1+4) / 100 3
= 5000 (`104 / 100` )3
= `(5000*104*104*104) / (100*100*100)` =5624.32dollars
A = 5624.32
Compound Interest = A – P = 5624.32 – 5000
= 624.32dollars.
Pro 4: Find the solution of simple interest, where total amount is 80,000, rate is 0.04 for per annum.
Sol: Simple interest = P*N*R.
=80000 *0.04 * 1.
=3200.
The simple interest is 3200.
Pro 5: Find the solution of simple interest, where total amount is 1,00,000, rate is 0.09 for per annum.
Sol: Simple interest = P*N*R.
=1,00,000 *0.09 * 1.
=9000.
The simple interest is 9000.
Simple interest
Compound interest
Simple interest: Simple interest is money we can earn by primarily investing some amount in bank or somewhere else (the principal). The percentage (the interest) of the principal amount is added to the principal, simple interest will increase our initial investments grow.
Compound interest: The difference between the original principal and the amount at the end of the last time period is known as the compound interest on the original principal period for that.
The important difference between compound and simple interest is that simple interest is paid only on the principal, whereas compound interest is paid on both the principal and the accumulated interest.
Interest formula
Simple interest formula:
The formula used for calculating the simple interest is
SI = `(PNR)/100`
Where,
P is the Principal,
N is the time period,
R is the rate of interest.
Compound interest formula:
The formula used for calculating the compound interest is
A = P (1 + `r / 100` )n
Where,
P is the Principal
R is the rate of interest
N is the number of years.
Solved Examples
Pro 1: Find the simple interest on an amount of $500 for one year at the rate of 6% per annum.
Sol: The formula is SI = PNR / 100
Principal (P) = $500
Rate of interest(r) = 6 % per annum
N= Interest on 100 dollar for 1 year = $6
Interest on 500 dollar for 1 year =6 / 100 × 500 = $30
Therefore the interest is $30.
Pro 2: Find the amount of and compound interest on $6000 for 3 years at 3% per annum.
Sol: Let p1, p2, p3… represents the principal for the first year, second year, third year and so on. Also let I1, I2, I3… represent interest for the first year, second year, third year and so on.
Understanding Definition of Compound Interest is always challenging for me but thanks to all math help websites to help me out.
The formula is A = P (1 +` r / 100` )n
C.I. = A – P
P = $6000, r = 3%, n = 3 years
A = P (1 + `r / 100` )` ^n ` = 6000 (1 + `3 / 100` )3
= 6000 (`103 / 100)` 3
= 6000 * 103 * 103 * 103 / 100 * 100 * 100
= 6556.36
Therefore
A = $6556.36
P = $6000
C. I. = A – P = 6556.36 – 6000 = 556.36
C. I. = $556.36
Pro 3: Find the amount and compound interest on 5000 dollars for 1.5 years at 8%per annum. Interest being is added to the principal every half year.
Sol: P = 5000dollars, n= 3 (three half years), r = `8/ 2` = 4%
A = P (1+`r / 100)` n = 5000 (1+4) / 100 3
= 5000 (`104 / 100` )3
= `(5000*104*104*104) / (100*100*100)` =5624.32dollars
A = 5624.32
Compound Interest = A – P = 5624.32 – 5000
= 624.32dollars.
Pro 4: Find the solution of simple interest, where total amount is 80,000, rate is 0.04 for per annum.
Sol: Simple interest = P*N*R.
=80000 *0.04 * 1.
=3200.
The simple interest is 3200.
Pro 5: Find the solution of simple interest, where total amount is 1,00,000, rate is 0.09 for per annum.
Sol: Simple interest = P*N*R.
=1,00,000 *0.09 * 1.
=9000.
The simple interest is 9000.
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