Quarterly Compound Interest with Worked Calculations
Quarterly Compound Interest is calculated by adding interest to the principal four times a year. The annual rate is divided by 4, while the number of years is multiplied by 4. This page covers the formula, calculation steps, solved numerical examples and useful shortcuts for aptitude questions.
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What Is Quarterly Compound Interest?
If the principal is P, the annual rate is R%, and the time is T years, the amount is calculated over 4T quarters. Thus, A = P(1 + R/400)^(4T), and compound interest is A − P. For example, on ₹10,000 at 8% per annum for 1 year, A = 10,000(1.02)^4 = ₹10,824.32, so the compound interest is ₹824.32.
Quarterly Compound Interest Video Lessons
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Compound Interest: Half-Yearly and Quarterly Compounding
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Quarterly Compound Interest Formula & Tricks
Important Formulas
P is the principal, R is the annual rate in percent, and T is time in years. The factor 4 represents four compounding periods per year.
Subtract the original principal from the quarterly compound amount to obtain compound interest.
Divide the annual percentage rate by 4 and multiply the time in years by 4.
When the time is M months and M is divisible by 3, the number of quarterly periods is M/3.
Quick Tricks
For quarterly compounding, divide the annual rate by 4. Do not use R/100 directly as the quarterly rate.
Multiply the time in years by 4 before applying the power.
For four quarters, calculate the quarterly factor successively instead of using annual compounding.
Quarterly Compound Interest Concepts
Quarterly Rate and Compounding Periods
If the annual rate is R%, each quarter earns R/4%. For T years, the total number of periods is 4T. For 18 months, the number of quarters is 18/3 = 6.
Calculating Amount and Compound Interest
The quarterly interest is added to the balance after every three months. Therefore, each later quarter earns interest on the increased balance from the previous quarter.
Quarterly Compounding for Months
The formula A = P(1 + R/400)^(M/3) applies when the time has complete three-month periods. For a duration such as 15 months, the exponent is 15/3 = 5.
Difference Between Simple and Quarterly Compound Interest
Simple interest for one year is PR/100. Quarterly compound interest is P[(1 + R/400)^4 − 1]. The difference occurs because each quarter's interest earns further interest in later quarters.
Quarterly Compound Interest Data Table
Use the structured data below while following the explanation and examples.
Annual Rate Converted to Quarterly Rate
Divide the nominal annual percentage rate by 4 to obtain the rate used for each quarter.
| Annual rate | Quarterly rate | Quarterly growth factor |
|---|---|---|
| 4% | 1% | 1.01 |
| 8% | 2% | 1.02 |
| 12% | 3% | 1.03 |
| 16% | 4% | 1.04 |
| 20% | 5% | 1.05 |
Note: The quarterly rate is expressed as a percentage; in the formula, R/400 is its decimal form.
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Quarterly Compound Interest Revision Points
Use these formulas and conversions when solving quarterly compounding questions.
- Quarterly compounding means four interest calculations per year.
- Quarterly rate = annual rate ÷ 4.
- Number of quarters = time in years × 4.
- A = P(1 + R/400)^(4T).
- CI = A − P = P[(1 + R/400)^(4T) − 1].
- For M months, the number of quarters is M/3 when the months form complete quarters.
- For one year, quarterly CI is P[(1 + R/400)^4 − 1].
Quarterly Compound Interest FAQs
What is the quarterly compound interest formula?
The formula is CI = P[(1 + R/400)^(4T) − 1], where P is principal, R is the annual rate in percent and T is time in years.
What quarterly rate is used for an annual rate of 12%?
The quarterly rate is 12% ÷ 4 = 3%. The quarterly growth factor is 1.03.
How many compounding periods are there in 3 years under quarterly compounding?
There are 3 × 4 = 12 quarterly periods.
Find the quarterly compound interest on ₹10,000 at 8% per annum for 1 year.
CI = 10,000[(1.02)^4 − 1] = ₹824.32. The amount is ₹10,824.32.
How is quarterly compound interest calculated for 18 months?
Convert 18 months into 18/3 = 6 quarters, then use A = P(1 + R/400)^6 and CI = A − P.
What is the difference between annual and quarterly compounding at the same nominal rate?
Annual compounding applies the full annual rate once, while quarterly compounding applies one-fourth of the annual rate four times. For a positive rate, quarterly compounding produces the larger amount because interest is added earlier and earns further interest.