For example, if you borrow $100 with an interest rate of 10% per year, you would pay $10 in interest per year if simple interest is used to calculate the interest amount. However, most lenders use compound interest which causes the interest amount to grow more rapidly over time. Albert Einstein famously referred to compound interest as the "most powerful force in the universe" because it has the potential to exponentially increase investment returns or accumulate debt.
What is Simple Interest?
Simple interest is a straightforward method of calculating the interest on a loan or investment by considering only the original amount borrowed or invested and the interest rate for the entire duration of the loan or investment. This type of interest is not compounded, meaning that interest is only calculated on the initial principal amount and not on any previously accrued interest. Simple interest is generally applied to shortterm loans or investments that have a duration of one year or less.
The formula for calculating simple interest involves the principal amount (P), the interest rate (R), and the duration of the loan or investment (T). The final amount to be paid is the sum of the principal amount and the simple interest, which is calculated using the formula SI = P x R x T / 100.
For Example: An invested sum fetched a total interest of $5000 at the rate of 10% in one year. What was the original principal amount?
Let principal amount be P, SI be simple interest, R be the rate of interest, and T the time period.
Accordingly,
SI = PRT/100
5000 = P × 10 × 1
P = 5000/10
P = 500
Hence, the original principal amount is $ 500.
Compound Interest
Compound Interest Formula
The formula for calculating the amount received when interest is compounded annually:
Amount = Principal (1 + Rate/100)
The total compounded interest over the term is calculated as
Compound Interest = Amount  Principal
Solved Example 1: In how many years will an amount of $2000 will be doubled, if the interest rate is 10% per annum?
Let the principal amount be P, R be the rate of interest per annum, SI be simple interest, and T be the time period.
Accordingly,
SI = PRT/100
2000 = 2000 × 10 × T ( because SI = P)
T = 20000/ 2000
T = 10 years
Hence, the amount of Rs.1000 will be doubled in 10 years.
Solved Example 2: What would be the amount Rs.100 in a year if the interest rate is 10% halfyearly ( every 6 months).
Let A be the amount received, P be the principal amount, R be the rate of interest per annum, SI be simple interest and T be time period.
Accordingly,
A = P (1 + R)T
= 100 × (1 + 10/100)²
= 100 × (21/20)²
= 100 × ( 441/400)²
= 441/4
= 110.25
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