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THE CONTENT PROVIDED ON THIS WEBSITE, INCLUDING ALL EXAM QUESTIONS, SOLUTIONS AND EXPLANATIONS RELATED TO SIMPLE AND COMPOUND INTEREST (Q1–Q400), IS PUBLISHED STRICTLY FOR EDUCATIONAL AND INFORMATIONAL PURPOSES ONLY. WHILE EVERY EFFORT HAS BEEN MADE TO ENSURE THE ACCURACY AND RELIABILITY OF THE QUESTIONS AND ANSWERS, THE WEBSITE OWNER DOES NOT CLAIM RESPONSIBILITY FOR ANY ERRORS, OMISSIONS OR DISCREPANCIES.
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(REFER TO YOUR SPECIFIC STATE PSC SITE)
INTRODUCTION:
ALBERT EINSTEIN ONCE SAID:
“COMPOUND INTEREST IS THE EIGHTH WONDER OF THE WORLD. HE, WHO UNDERSTANDS IT, EARNS IT; HE WHO DOESN’T, PAYS IT.”
COMPOUNDING IS A POWERFUL FINANCIAL CONCEPT THAT HELPS YOUR MONEY GROWS FASTER OVER TIME. IN THIS ARTICLE, WE EXPLAIN THE DIFFERENCE BETWEEN SIMPLE INTEREST (SI) AND COMPOUND INTEREST (CI), THEIR FORMULAS AND HOW TO CALCULATE THEM WHEN INTEREST IS COMPOUNDED MONTHLY, QUARTERLY, HALF-YEARLY OR BIMONTHLY — ALL WITH REAL EXAMPLES.
WHAT IS SIMPLE INTEREST (SI)?
SIMPLE INTEREST IS CALCULATED ON THE ORIGINAL PRINCIPAL AMOUNT FOR THE ENTIRE INVESTMENT PERIOD.
SI FORMULA:
SI=P×R×T/100
WHERE:
P = PRINCIPAL
R = RATE OF INTEREST (PER ANNUM)
T = TIME IN YEARS
EXAMPLE (SIMPLE INTEREST):
IF YOU INVEST ₹10,000 AT 10% ANNUAL INTEREST FOR 2 YEARS:
SI=10000×10×2/100=₹2000
TOTAL AMOUNT = ₹10,000 + ₹2000 = ₹12,000
WHAT IS COMPOUND INTEREST (CI)?
COMPOUND INTEREST MEANS INTEREST ON INTEREST. UNLIKE SI, THE INTEREST IS ADDED TO THE PRINCIPAL AND FUTURE INTEREST IS CALCULATED ON THIS UPDATED AMOUNT.
GENERAL CI FORMULA:-
A = P ( 1 + R / (n x 100))n x T
CI = A – P
WHERE:
A = FINAL AMOUNT
P = PRINCIPAL
R = ANNUAL INTEREST RATE
T = TIME IN YEARS
n = NUMBER OF TIMES INTEREST COMPOUNDED PER YEAR
COMPOUNDING FREQUENCIES AND FORMULAS
| FREQUENCY | VALUE OF N | FORMULA FOR CI |
| ANNUALLY | 1 | A = P ( 1 + R / 100)T |
| HALF-YEARLY | 2 | A = P ( 1 + R / (2 x 100)) 2 x T |
| QUARTERLY | 4 | A = P ( 1 + R / (4 x 100)) 4 x T |
| BIMONTHLY | 6 | A = P ( 1 + R / (6 x 100)) 6 x T |
| MONTHLY | 12 | A = P ( 1 + R / (12 x 100)) 12 x T |
REAL-LIFE EXAMPLE (COMPOUND INTEREST ON ₹10,000 FOR 1 YEAR AT 12% RATE)
LET’S CALCULATE THE FINAL AMOUNT WITH DIFFERENT COMPOUNDING FREQUENCIES.
| COMPOUNDING FREQUENCY | FORMULA USED | FINAL AMOUNT (₹) | CI EARNED (₹) |
| ANNUALLY | 10000 (1 + 12/100)1 | ₹11,200 | ₹1,200 |
| HALF-YEARLY | 10000 (1 + 6/100)2 | ₹11,236 | ₹1,236 |
| QUARTERLY | 10000 (1 + 3/100)4 | ₹11,255.09 | ₹1,255.09 |
| BIMONTHLY | 10000 (1 + 2/100)6 | ₹11,266.82 | ₹1,266.82 |
| MONTHLY | 10000 (1 + 1/100)12 | ₹11,268.25 | ₹1,268.25 |
CONCLUSION:-
MORE FREQUENT COMPOUNDING = HIGHER RETURNS OVER TIME!
KEY TAKEAWAYS
SIMPLE INTEREST GROWS IN A STRAIGHT LINE.
COMPOUND INTEREST GROWS EXPONENTIALLY.
MONTHLY OR FREQUENT COMPOUNDING EARNS MORE.
THE EARLIER YOU START, THE BIGGER YOUR GAINS.
USE CI FOR LONG-TERM INVESTMENTS LIKE SIPS, FDS, AND RETIREMENT FUNDS.
RULE OF 72: THE SHORTCUT TO DOUBLING YOUR MONEY
THE RULE OF 72 IS A SIMPLE FORMULA USED TO ESTIMATE THE NUMBERS OF YEARS IT TAKES FOR AN INVESTMENT TO DOUBLE IN VALUE AT AFFIXED ANNUAL RATE OF INTEREST TO FIND OUT THE RATE NEEDED TO DOUBLE IN A GIVEN TIME.
THIS RULE IS POPULARLY USED IN FINANCE, BANKING AND COMPETITIVE EXAMS FOR QUIXK MENTAL CALCULATIONS INVOLVING COMPOUND INTEREST AND INVESTMENT GROWTH.
RULE OF RULE 72 FORMULAE:
TO CALCULATE TIME TO DOUBLE
TIME (YEARS) =72 / INTEREST RATE (% PER ANNUM)
TO CALCULATE RATE OF RETURN
INTEREST RATE (% PER ANNUM) = 72 / TIME (YEARS)
EXAMPLES:-
DOUBLING TIME:
IF YOUR INVESTMENT EARNS 8% ANNUAL RETURN THEN:
TIME = 72 / 9 = 8 YEARS
REQUIRED RATE:-
IF YOUR MONEY WANT TO DOUBLE IN 6 YEARS, THEN
RATE = 72 / 6 =12%
LIMITATIONS:-
IT`S AN APPROXIMATIONS, NOT EXACT MATH.
BEST FOR INTEREST RATE BETWEEN 6% AND 10%.
FOR HIGH RATES (ABOVE 15%), RESULTS MAY VARY.
