Observing our bank statements, we get credit for some interest every year. In our everyday life, compound interest is a very commonly used concept. For a given principal amount, the interest charged by the bank varies with each year. We can see that interest increases over successive years. Consequently, it cannot be called simple interest, but rather compound interest. The objective of this article is to introduce you to the concept of compound interest, to provide you with CI formulas to determine CI annually, half-annually, quarterly, etc. In addition, following the examples based on real-life applications of compound interest, one can understand why it is higher than simple interest.
An interest rate that is calculated using both the principal and the interest accumulated over the previous period is compound interest. A compound interest calculation differs from simple interest, where interest is not added to the principal when calculating the following period’s interest. It can be found in most financial transactions, especially those involving banks and financial institutions. The compound interest formula can be used to ease calculations in math for compound interest. It is calculated by dividing the amount by the principal.
The formula for compound interest:
Compound Interest = Amount – Principal
Where,
A = amount
P = principal
R = rate of interest
N = number of times interest is compounded per year
T = time (in years)
And
CI = P(1+r/n)nt −P
This compound interest formula is also called the periodic compounding formula.
- Following compounding, A symbolizes the new principal sum or the total value of the loan
- Original amounts or initial amounts are represented by P
- A rate of interest is represented by r
- A compounding frequency of n represents the number of times interest has compounded each year
- T represents the number of years
As noted above, the above formula is a general method of calculating the number of times the principal is compounded in a calendar year. If the interest is compounded annually, the calculation is as follows:
A=P(1+R/100)t
For the first year, compound interest has the same rate as simple interest. PR/100. In subsequent years, the compounded interest rates will always be greater than simple interest.
Examples:
- A town had 5,000 residents in 2010. Its population declines at a rate of 10% per annum. What will be its total population in 2015?
Ans: Every year, the population of the town decreases by 10%. Then, every year it is re-populated. Therefore, the population for the following year is based on the population of this year.
For the decrease, we have the formula A = P(1 – R/100) n
Therefore, the population at the end of 5 years = 5000(1 – 10/100)5
= 5000(1 – 0.1)5 = 5000 x 0.95 = 4750
- The count of a certain breed of bacteria was found to increase at the rate of 4% per hour. Find the bacteria at the end of 2 hours if the count was 800000.
Ans: Since the population of bacteria increases at the rate of 4% per hour, we use the formula
A = P(1 + R/100)n
Thus, the population at the end of 2 hours = 800000(1 + 4/100)2
= 800000(1 + 0.04)2 = 800000(1.04)2 = 865280
- The price of a radio is Rs. 1000 and it depreciates by 5% per month. Find its value after 3 months.
Ans: For the depreciation, we have the formula A = P(1 – R/100) n
Thus, the price of the radio after 3 months = 1000(1 – 5/100)3
= 1000(1 – 0.05)3 = 1000 (0.95)3 = Rs. 858 (Approx.)
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