Do you feel any difficulty in calculating the Compound Interest? Not anymore after going through this article. Finding Compound Interest using the Formula is quite simple and you don’t have to do hectic calculations, unlike the manual methods. You just need to substitute the inputs and perform basic maths to obtain the Calculate Compound Interest instantly.
For the sake of your convenience, we have listed the Formulas for finding Compound Interest Annually, Half-Yearly, Quarterly along with Solved Examples. Refer to the Step by Step Solutions provided and understand the concept easily.
Compound Interest Formula in Different Cases
In general, Compound Interest is the Interest calculated on the Principal and the Interest accumulated over the previous period. We have listed the Compound Interest Formulas in various cases like When Interest Rate is Compounded Annually, Half-Yearly, Quarterly in the coming modules by taking enough examples.
- Compound Interest Formula when Rate is Compounded Annually
- Compound Interest when Rate is Compounded Half-Yearly
- Compound Interest Quarterly Formula
- When the Interest is Compounded Annually but rates are different for different years
- Interest is compounded annually but time is a fraction
Annually Compound Interest Formula
We know the Formula to Calculate the Amount is A = P(1+r/n)nt
Where A= Amount
P= Principal
R= Rate of Interest
n= Number of times interest is compounded per year
If the Interest Rate is Compounded Annually we have the Formula as A = P(1+R/100)t
CI = A – P
Examples
1. Find the amount of $4000 for 2 years, compounded annually at 5% per annum. Also, find the compound interest?
Solution:
We know the formula to calculate Amount is A = P(1+R/100)n
P = $4000, R = 5%, n = 2 years
Substitute the input data we get the equation as such
A = 4000(1+5/100)2
= 4000(105/100)2
= $4410
CI = A – P
= $4410- $4000
= $410
Therefore, Compound Interest is $410.
2. Calculate the compound interest (CI) on Rs. 3000 for 1 year at 10% per annum compounded annually?
Solution:
The Formula to Calculate the Amount is A = P(1+R/100)n
P = Rs. 3000, n = 1 year R = 10%
Substituting the input data in the formula and we get
A = 3000(1+10/100)1
= 3000(1.1)
= Rs. 3300
CI = A – P
= 3300 – 3000
= Rs. 300
Half-Yearly Compound Interest Formula
Let us calculate the Compound Interest on a Principal P kept for 1 Year and at an Interest Rate R% compounded half-yearly
As the Interest is compounded half-yearly Interest Amount will vary after the first 6 months. The Interest for the next 6 months will be calculated on the remaining amount after the first 6 months.
Principal = P, Rate = R/2 %, Time = 2n
A = P(1+R/100)n
Substitute R/2 and 2n in terms of Rate and Time in the above formula
A = P(1+R/2*100)2n
CI = A – P
Example
Calculate the compound interest to be paid on a loan of Rs. 20,000 for 3/2 years at 10% per annum compounded half-yearly?
Solution:
From the given data
Principal = 20,000
R = 10%
n = 3/2
A= P(1+R/2*100)2n
Substitute the input values in the formula and we have
A = 20,000(1+10/200)2*3/2
= 20, 000(1+10/200)3
= 20,000(1.157)
= Rs. 23152
CI = A – P
= 23,152 – 20,000
= Rs. 3152
Compound Interest Quarterly Formula
Let us find the Compound Interest Kept on a Principal for 1 year and a Rate of R% compounded quarterly. Since CI is compounded quarterly principal amount will change after the first 3 months. The next 3 months(second quarter) interest will be calculated on the amount left after the first 3 months. Third-quarter Interest will be calculated on the amount left after the first 6 months. Last quarter will be found on the amount left after the first 9 months.
The formula of Compound Interest Compounded Quarterly is given as
A = P(1+R/4/100)4n
CI = A – P
Example
Find the compound interest on $12,000 if Nick took a loan from a bank for 6 months at 8 % per annum, compounded quarterly?
Solution:
From the given data P = $12, 000
R = 8% per Annum, (8/4)% per quarter = 2% per quarter
T = 6 months = 2 Quarters
A = P(1+R/100)n
= 12,000(1+2/100)2
= 12,000(1+0.02)2
= 12,000(1.02)2
= Rs. 12,484
CI = A – P
= 12,484 – 12,000
= Rs. 484
When the Interest is Compounded Annually but rates are different for different years
Suppose the Interest Compounded Annually be different in different years. In the first year if the Interest Rate is p % per annum and for the second year if it is q % then
Amount Formula is given by = P*(1+p/100)*(1+q/100)
This formula can be extended for any number of years.
To get the Compound Interest Subtract Principal from Amount i.e. CI = A – P
Example
Find the amount of $10, 000 after 2 years, compounded annually, if the rate of interest being 3 % p.a. during the first year and 4 % p.a. during the second year. Also, find the compound interest?
Solution:
Formula to Calculate the Amount is A = P*(1+p/100)*(1+q/100)
From the given data P = $10, 000, p = 3%, q = 4%
Substitute the inputs in the formula to calculate the Amount and the equation is as under
A = 10,000(1+3/100)(1+4/100)
= 10, 000(1.03)(1.04)
= $10712
CI = A – P
= $10712 – $10, 000
= $712
Interest is Compounded Annually but time is a fraction
For instance, if time is 5 3/4 years then Amount is given as under
A = P * (1 + R/100)5 * [1 + (3/4 × R)/100]
Example
Find the compound interest on $ 30,000 at 6 % per annum for 3 years. Solution Amount after 3 3/4 years?
Solution:
Amount after 3 3/4 years is given by A = $ [30,000 × (1 + 6/100)3 × (1 + (3/4 × 8)/100)]
= $[30,000 * (1 + 0.06)3 * (1 + 6/100)]
=$[30,000*(1.06)3*(1.06)]
= $37874
CI = A – P
= $37874 – $30, 000
= $874
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