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# Quarterly Compound Interest Formula

• Last Updated : 07 Dec, 2022

Interest is the additional money we pay for the use of some other person’s money. When we borrow some amount of money from a person or organization we give them additional money as an incentive for it, this additional sum of money is called Interest. The amount of money you initially lend is called the principal and the duration of that loan is called the time period. For Example, if you pay 2000 in interest for a loan of 20,000 this means the interest is 2000 and the principal is 20,000 and the rate of interest is 10 percent.

Based on the type of repayment Interest can be classified as mainly two types:

• Simple Interest
• Compound Interest.

## Simple Interest

Simple interest is the basic Interest rate, The interest is calculated only on the given principal once or over a period of many years without considering the interest earned in the principal. Simple interest is paid only on the principal amount and it is not compounded. The formula for simple interest is

Simple Interest (SI) = (P×R×T)/100

where,
P is the principal
R is the rate of Interest
T is the time period

## Compound Interest

This type of interest rate is more commonly used in the real life. The loans given as investments are mostly given in this method of payment. In this type, the interest is not calculated not only for the principal but the last term’s interest is also added to the principal and is then calculated. The interest is compounded over the principal. The interest can even be calculated half-yearly, quarterly, yearly, or even daily.

For Example, if you pay 2000 in interest for a loan of 20,000 in the first year then for the next year the principal is 22,000.

The Amount received after one year of compound interest is

Amount = Principal (1 + Rate/100)Time

Compound Interest = Amount – Principal

General Compound interest formula is

Amount = P [1 + R/(100×n)]t×n

where,
P is the principal
R is the rate of Interest
n is the number of times it is compounded in a year
t is the time period in years.

Compound Interest = P [1 + R/(100×n)]t×n – P

Compound Interest can be calculated quarterly, monthly, or even daily.

## Quarterly Compound Interest

In this case, the general equation remains the same, there is change only in the value of n

Here, n is equal to 4

Compound Interest = P (1 + R/400)4t – P

Amount = P (1 + R/400)4t

Example: What will be the amount needed to pay for the amount of 10,000 if it is taken as a loan for 5 years at a 2 percent rate compounding quarterly

Solution:

Amount = P (1 + R/100×n)t×n

Principal= 10,000
Rate of Interest = 2
n = 4
Time period = 5 years

Amount = P (1 + R/100×n)t×n
Amount = 10,000(1 + 2/400)5×4
Amount = 11,048.9557

Thus, the amount paid at the end of 5 years is ₹ 11,048.9557

## Solved Examples on Quarterly Compound Interest

Example 1: What is the amount that needs to be paid back after 3 years if the money of 20,000 was taken at a rate of 6 percent and it is compounded annually?

Solution:

Principal = 20,000
Rate of Interest = 6
n = 1
Time Period = 3 years

Compound Interest = P (1 + R/100×n)t

Amount = 20,000(1 + 6/100)3
Amount= 20,000(1 + 6/100)3
Amount= 23820.32

So, the amount to be paid after 3 years = ₹23820.32.

Example 2: What will be the quarterly compound interest on the amount of 4000 if the number of years is 2 and the interest rate is 8 percent?

Solution:

Principal = 4000
Rate of Interest = 8
n = 4
Time period = 2 years

Compound Interest = P (1 + R/100×n)t*n – P

CI = 4000(1 + 8/4× 100)2*4 – 4000
CI = 4000(1 + 8/400)8 – 4000
CI = 4686.63 – 4000
C I= 686.63

Example 3: What will be the interest to be paid after 5 years for an amount of 10,00,000 at a rate of 5 percent if it is simple interest?

Solution:

Simple Interest (SI) = (P×R×T)/100

P= 10,00,000
R= 5 percent
T= 5

SI= (10,00,000 × 5 × 5)/100
SI= 10,000 × 25
SI= 2,50,000

Therefore, the interest to be paid is ₹2,50,000

Example 4: If the borrower returns 12,000 in interest after 2 years at 2 percent interest calculate the principal amount.

Solution:

Simple Interest (SI) = (P×R×T)/100

SI = 12,000
R = 2percent
T = 2 years

12,000 = (P × 2 × 2)/100
12.00,000 = 4 × P
12,00,000 /4 = P
3,00,000 = P

Therefore, the principal amount is ₹3,00,000

Example 5: What will be the quarterly compound interest on the amount of 50,000 if the number of years is 2 and the interest rate is 5 percent?

Solution:

Principal = 50,000
Rate of Interest = 5
n = 4
Time period = 1 year

Compound Interest = P (1 + R/100×n)t×n – P

CI = 50,000(1 + 5/400)2×4 – 50,000
CI= 55,224.30 – 50,000
CI= 5224.30

Example 6: If the borrower returns 10,000 in interest compounded annually after 5 years at 6 percent interest calculate the principal amount.

Solution:

Simple Interest (SI) = (P×R×T)/100

SI= 10,000
R=  6 percent
T= 5 years

10,000 = (P × 6 × 5)/100
10,00,000 = 30 × P
10,00,000 / 30 = P
33,333.33 = P

Therefore, the principal amount is ₹33,333.33.

Example 7: What is the amount that needs to be paid back after 4 years if the money of 30,000 was taken at a rate of 5 percent and it is compounded annually?

Solution:

Principal = 30,000
Rate of Interest = 5
n = 1
Time Period = 4 years

Compound Interest = P (1 + R/100×n)4

Amount = 30,000(1 + 5/100)4
Amount= 30,000(1 + 5/100)4
Amount= 36,465.187

So, the amount to be paid after 4  years is ₹36,465.187

## FAQs on Quarterly Compound Interest

Question 1: What is Interest and what are the types?

Interest is the additional money we pay for the use of some other person’s money. When we borrow some amount of money from a person or organization we give them additional money as an incentive for it, this additional sum of money is called Interest. The amount of money you initially lend is called the principal and the duration of that loan is called the time period.

Question 2: What is Simple Interest?

Simple interest is calculated only on the given principal once or over a period of many years without considering the interest earned in the principal. Simple interest is paid only on the principal amount. The formula for simple interest is: Simple Interest (SI) = (P×R×T)/100

Question 3: What is Compound Interest?