Compound Interest is an important concept used in our day-to-day life. It is defined as the interest amount imposed on a deposit or loan amount. This concept is used for all financial and business transactions and its power can be understood by observing the values accumulated across regular time periods.
Compound Interest by using the formula is simple and doesn’t need heavy calculations like manual methods. Here you can find the formulas for compound interest annually, half-yearly, and quarterly. Refer to the below article to understand the 10th Grade Math concept more clearly.
Also, find
- Practice Test on Compound Interest
- Introduction to Compound Interest
- Compound Interest as Repeated Simple Interest
What is Compound Interest?
It is the interest that is calculated on the principal and interest accumulated over the previous period. It is generally denoted by C.I. If we observe the bank statements, we will notice that the interest is credited to the account every year. The interest credited varies each year with the same principal amount and it increases for successive years. The applications of compound interest are:
- Decrease or Increase in population.
- Growth of bacteria.
- Depreciation or Rise in the value of an item.
Compound Interest Yearly Formula | Compound Interest when Compounded Yearly
The compound interest formula when calculated yearly, the formula is:
Let Principal = $P, Rate = R% per annum and Time = n years
The formula for the amount to be calculated is
Case 1:
The interest is compounded annually: CI = P{(1 + \(\frac { r }{ 100 } \))n}
Case 2:
Let Principal = $P, Time = 2 years, and let the rates of interest be p% per annum during the first year and q% per annum during the second year.
The amount after 2 years = ${P * (1+ P/100) * (1+ q/100)}
The formula will be extended for any number of years.
Case 3:
The interest is compounded annually but time is the fraction
Amount = P * (1 + R/100)² * [1 + (T * R)/100]
Compound Interest Half-Yearly Formula
Calculating the compound interest on a principal P for 1 year and the interest rate R% is compounded half-yearly.
As the interest is compounded half-yearly, the principal amount changes after the end of the first half of the year.
Let principal = $P, Rate = R% per annum, Time = n years
The interest is compounded half-yearly,
Then rate = (R/2)% per half-year, Time = (2n) half-years
CI = P{(1 + \(\frac { r }{ 2 * 100 } \))2n}
Compound Interest = Amount – Principal
Compound Interest Quarterly Formula
Calculating the compound interest on a principal P for 1 year and the interest rate R% is compounded quarterly.
As the interest is compounded half-yearly, the principal amount changes after the end of the first quarter of the year.
Let principal = $P, Rate = R% per annum, Time = n years
The interest is compounded quarterly,
Then rate = (R/4)% per quarter time = (4n) quarters
CI = P{(1 + \(\frac { r }{ 4 * 100 } \))4n}
Compound Interest = Amount – Principal
Compound Interest Formula Examples with Solutions
Be the first to practice all the questions and check out the answers. Find the complete explanation to learn the tricks.
Example 1:
Find the amount of $10,000 for 4 years, compounded annually at 8% per annum. Also, find the compound interest?
Solution:
Given that,
P = $10,000, R = 8% per annum and n = 4 years
We use the formula, CI = P{(1 + \(\frac { r }{ 100 } \))n}
Amount after 4 years = ${10000 * 〖(1 + 8/100)4}
= ${10,000 * 1.08 * 1.08 * 1.08 * 1.08}
= $13,604.8
Therefore, the amount after 3 years = $13,604.8
Compound Interest = Amount – Principal
= 13,604.8 – 10,000
= $3604.8
Therefore, the compound interest = $3604.8
This problem is the example of case 1 situation in the Compound Interest Formula for Yearly.
Example 2:
Find the amount of $15,000 after 2 years, compounded annually, the rate of interest is 7% per annum during the first year and 8% per annum during the second year. Also, find the compound interest?
Solution:
Given that,
Principal = $15,000, p = 7% per annum and q = 8% per annum
We use the formula
A = {P * (1 + p/100) * (1 + q/100)}
Amount after 2 years = ${15000 * (1 + 7/100) * (1 + 8/100)}
= $(15000 * 1.07 * 1.08)
= $ 17,334
Thus the amount after 2 years = $17334
Compound Interest = Amount – Principal
= $(17,334 – 15,000)
= $2,334
Therefore, the compound interest = $1356
This problem is the example of case 2 situation in the Compound Interest Formula for Yearly.
Example 3:
Find the compound interest of $30,000 at 10% per annum for 2 years. Find the amount after
2 3/4years?
Solution:
Given that, Principal = $30,000, Amount after 23/4years is
= P * (1 + R/100)² * [1 + (T * R)/100]
= $ [30,000 * (1 + 10/100)^2 * [1 + (¾ * 8)/100)]
= $ {30,000 * (1.1)^2 * (53/50)}
= $ {30,000 * 1.1 * 1.1 * 1.06}
= $ 38,478
Therefore, the amount = $38,478
Compound Interest = Amount – Principal
= $ 38,478 – 30,000
= $ 8,478
Therefore, the compound interest = $ 8,478
This problem is the example of case 3 situation in the Compound Interest Formula for Yearly.
Example 4:
Find the compound interest on $1,50,000 for 3 years at 8% per annum when compounded semi-annually?
Solution:
Given that, Principal = $1,50,000, Rate = 8% per annum = 4% per half-year, Time = 3 years which is equal to 6 half years.
Amount = ${150000 * (1 + 4/100)6}
= ${150000 * 26/25 * 26/25 * 26/25 * 26/25 * 26/25 * 26/25}
= $ {150000 * 1.04 * 1.04 * 1.04 * 1.04 * 1.04 * 1.04}
= $ (1,89,797.85}
Therefore, the amount = $ (1,89,797.85}
Compound Interest = Amount – Principal
= $ 1,89,797.85 – 1,50,000
= $ 39,797.85
Therefore, the compound interest = $ 39,797.85
Example 5:
Find the compound interest on $1,15,000, if Milley took a loan from a bank for 12 months at 8% per annum, compounded quarterly?
Solution:
Given that, Principal = $1,15,000
Rate = 8% per annum = (8/4)% per quarter = 2% per quarter
Time = 12 months = 4 quarters
Therefore, Amount = $ {1,15,000 * (1 + 2/100)^4}
= $ {1,15,000 * 51/50 * 51/50 * 51/50 * 51/50}
= $ 1,24,479.69
Therefore, the amount = $ 1,24,479.69
Compound Interest = Amount – Principal
= $ 1,24,479.69 – 1,15,000
= $ 9479.69
Therefore, the compound interest = $ 9479.69
FAQs on Formula for Compound Interest
1. What is the formula for compound interest?
The formula for calculating compound interest is A = P(1 + r/n)^nt. A represents the amount of your principal along with interest which is the total amount.
2. How compound interest depends on the time period?
The compound interest depends on the calculation of the interest time interval. The time interval can be a day, a week, a month, quarterly, half-yearly, or 6 months, annual. For the calculation of shorter time periods, the net cost is higher.
3. Can the principal amount be lesser than compound interest?
The principal is lesser than compound interest. The compound interest amount increases and varies for various time periods. The initial principal of $200 was invested over a time period of $20, $21, $ 22.1, and $ 23.32 over the period of 1 year. Hence, the compound interest increases overtime a period and can be greater than the principal value.
4. What is the main information required to calculate compound interest
The calculation of compound interest, it requires various factors like rate of interest, principal, and time period. Time intervals should also be known to calculate the interest.
Summary
Compound Interest by using the Formula concept is included here according to the latest syllabus. This entire article offers complete information regarding the formula of the compound interest and related problems. Without any delay, quickly start your practice now.