Quarterly Compound Interest Formula (original) (raw)

Last Updated : 23 Jul, 2025

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.

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

**Simple interest is the interest calculated only on the original principal amount, using the formula:

**SI = P × R × T/100

Where P is the principal, R is the annual rate of interest, and T is the time in years.

**Compound interest is the interest calculated on the initial principal and the accumulated interest from previous periods, leading to exponential growth. It is given by the formula:

**Amount = P (1 + r/n) nt
**Compound Interest = A - P

Where r is the rate of interest, P is the principal, and n is the number of compounding periods.

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

**Quarterly Compound Interest

**Quarterly compound interest is the interest calculated and added to the principal four times a year, at the end of each quarter. It grows faster than annual compounding because the interest is compounded more frequently.

In this case, the general equation remains the same, there is a change only in the value of **n.
Here, n is equal to 4 and the formula becomes:

**Compound Interest = P (1 + R/400) 4t - P
**Amount = P (1 + R/400) 4t

Solved Examples of **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