Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
If at same rate of interest, in 2 years, the simple interest is тВ╣56 and compound interest is тВ╣64, then what is the principal (in тВ╣)?
93
98
91
102
98
In this problem, the Simple Interest (SI) for 2 years is тВ╣56, meaning the interest for 1 year is тВ╣28. Since Compound Interest (CI) accounts for interest on the interest earned in the first year, the difference between CI and SI for 2 years represents the interest earned on the first year's interest (PnewтАЛ=Iyear1тАЛ).
In this problem, the Simple Interest (SI) for 2 years is тВ╣56, meaning the interest for 1 year is тВ╣28. Since Compound Interest (CI) accounts for interest on the interest earned in the first year, the difference between CI and SI for 2 years represents the interest earned on the first year's interest (PnewтАЛ=Iyear1тАЛ).
Think of it like a snowball rolling downhill: Simple Interest is the original size of the ball added each lap, while Compound Interest includes the extra snow stuck to the sides of the new layers added previously.
SI=100P├ЧR├ЧTтАЛ тАФ Simple Interest formula
CIтИТSI=P├Ч(100RтАЛ)2 тАФ Difference for 2 years
The principle P is calculated by noting that the excess interest in CI comes from the interest earned on the first year's simple interest. Given SI2тАЛ=56, then SI1тАЛ=28. The difference CI2тАЛтИТSI2тАЛ=64тИТ56=8. This difference of тВ╣8 is the interest earned on the principal amount that equals the first year's SI (тВ╣28) at the same rate R. Thus, 8=28├Ч(R/100), giving R=800/28=200/7%. Substituting this back into the SI formula: 28=P├Ч(200/700)├Ч1, which yields P=28├Ч3.5=98.
Simple interest remains constant every year for a fixed principal.
The difference between CI and SI for 2 years is always the interest earned on the first year's interest.
Rate R=Interest┬аper┬аyearDifferenceтАЛ├Ч100.
Provides a clear mathematical relationship between simple and compound growth.
Requires careful algebraic manipulation if the rate is not an integer.
Banking and financial planning
Loan repayment analysis
The rate of interest in this specific problem is approximately 28.57% per annum.
Option B (98) is the only value satisfying the 2-year interest accumulation criteria.
B is correct тАФ Using the difference formula for 2 years, we find the principal is тВ╣98.
Whenever you see a difference between CI and SI for 2 years, always treat it as interest earned on the first year's simple interest to solve for R quickly.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download тАв 100K+ Aspirants