Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
If the simple interest on a sum of money at 8% per annum in 2 years is ₹2,000, find the compound interest on the same sum for the same period at the same rate in case of annual compounding.
₹2,080
₹2,040
₹1,960
₹1,660
₹2,080
For 2 years, the difference between Compound Interest and Simple Interest is CI−SI=SI×200R. Here, 2000×2008=80, so CI=2000+80=2080.
Simple Interest (SI) = ₹2,000, Time (T) = 2 years, Rate (R) = 8% per annum.
CI−SI=P×(100R)2
For 2 years, the difference between Compound Interest and Simple Interest is CI−SI=SI×200R. Here, 2000×2008=80, so CI=2000+80=2080.
Students often calculate the Principal first and then find CI using P(1+R/100)n−P, which is significantly slower than using the direct difference formula.
Calculate Simple Interest for one year
Since Simple Interest is ₹2,000 for 2 years, the interest for 1 year is half of it: SI1=2000/2=1000.
SI1=1000
Calculate the difference
Compound Interest for 2 years includes the simple interest for 2 years plus the interest on the interest of the first year. The extra interest is 8% of the first year's interest: 8% of 1000=0.08×1000=80.
Difference=80
Calculate total Compound Interest
Total CI is SI+Difference=2000+80=2080.
CI=2080
A is correct because the compound interest is the sum of the simple interest (₹2,000) and the additional interest earned on the first year's interest (₹80), totaling ₹2,080.
This difference formula method works for any 2-year duration problem involving interest differences. It is also useful in profit/loss and percentage change questions.
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 • 100K+ Aspirants