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DISCLAIMER
THE CONTENT PROVIDED ON THIS WEBSITE, INCLUDING ALL EXAM QUESTIONS, SOLUTIONS AND EXPLANATIONS RELATED TO SIMPLE AND COMPOUND INTEREST (Q1โQ400), 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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THE QUESTIONS PROVIDED ON THIS WEBSITE ARE BASED ON PAST YEAR PAPERS AND MOCK FORMATS FROM COMPETITIVE EXAMS. FOR AUTHENTIC VERIFICATION, USERS ARE ENCOURAGED TO VISIT THE OFFICIAL WEBSITES OF THE RESPECTIVE CONDUCTING BODIES:
STAFF SELECTION COMMISSION (SSC)
OFFICIAL PORTAL: ๐ https://ssc.nic.in
COVERS: SSC CGL, CHSL, MTS, GD, JE, ETC.
INSTITUTE OF BANKING PERSONNEL SELECTION (IBPS)
OFFICIAL PORTAL: ๐https://www.ibps.in
COVERS: IBPS PO, CLERK, RRB PO/CLERK, SO, ETC.
STATE BANK OF INDIA (SBI) โ RECRUITMENT
OFFICIAL PORTAL: ๐ https://sbi.co.in/web/careers
COVERS: SBI PO, SBI CLERK, SBI SO
RAILWAY RECRUITMENT BOARDS (RRB)
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ZONE-WISE SITES LINKED FROM THE MAIN PORTAL
COVERS: RRB NTPC, RRB ALP, RRB JE, ETC.
UNION PUBLIC SERVICE COMMISSION (UPSC)
OFFICIAL PORTAL: ๐https://upsc.gov.in
COVERS: NDA, CDS, CAPF, CIVIL SERVICES, ETC.
LIFE INSURANCE CORPORATION OF INDIA (LIC)
CAREERS PAGE: ๐ https://licindia.in/bottom-links/careers
COVERS: LIC AAO, ADO, ASSISTANT EXAMS
STATE PUBLIC SERVICE COMMISSIONS (PSC)
EXAMPLES:
UTTAR PRADESH: ๐ https://uppsc.up.nic.in
MAHARASHTRA: ๐https://mpsc.gov.in
TAMIL NADU: ๐https://www.tnpsc.gov.in
(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 DOESNโT, 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 โ 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=PรRรT/100โ
WHERE:
P = PRINCIPAL
R = RATE OF INTEREST (PER ANNUM)
T = TIME IN YEARS
EXAMPLE (SIMPLE INTEREST):
IF YOU INVEST โน10,000 AT 10% ANNUAL INTEREST FOR 2 YEARS:
SI=10000ร10ร2/100โ=โน2000
TOTAL AMOUNT = โน10,000 + โน2000 = โน12,000
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 โน10,000 FOR 1 YEAR AT 12% RATE)
LETโS CALCULATE THE FINAL AMOUNT WITH DIFFERENT COMPOUNDING FREQUENCIES.
| COMPOUNDING FREQUENCY | FORMULA USED | FINAL AMOUNT (โน) | CI EARNED (โน) |
| ANNUALLY | 10000 (1 + 12/100)1 | โน11,200 | โน1,200 |
| HALF-YEARLY | 10000 (1 + 6/100)2 | โน11,236 | โน1,236 |
| QUARTERLY | 10000 (1 + 3/100)4 | โน11,255.09 | โน1,255.09 |
| BIMONTHLY | 10000 (1 + 2/100)6 | โน11,266.82 | โน1,266.82 |
| MONTHLY | 10000 (1 + 1/100)12 | โน11,268.25 | โน1,268.25 |
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.
