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If at same rate of interest, in 2 years, the simple interest is ₹56 and compound interest is ₹72, then what is the principal (in ₹)?
53
42
49
44
49
In a 2-year period, the simple interest (SI) for the first year is exactly half of the total SI, while the compound interest (CI) includes the interest earned on the interest from the first year. The difference between CI and SI for 2 years represents the interest accrued on the first-year interest, which allows us to determine the annual rate of interest.
In a 2-year period, the simple interest (SI) for the first year is exactly half of the total SI, while the compound interest (CI) includes the interest earned on the interest from the first year. The difference between CI and SI for 2 years represents the interest accrued on the first-year interest, which allows us to determine the annual rate of interest.
Think of Simple Interest as a fixed rental fee, while Compound Interest is like a 'tax on your earnings'—where you start paying interest on the interest you've already accumulated in the second year.
SI=100P×R×T — Simple Interest formula
CI=P(1+100R)T−P — Compound Interest formula
Difference=P(100R)2 — Shortcut for 2 years
The simple interest SI for 2 years is 2×P×R×T (or simply 2×SI1). Since SI for 2 years is ₹56, the SI for one year is ₹28. The difference between CI and SI for two years, d=CI−SI, equals the interest earned on the first year's interest: d=100SI1×R. Given d=72−56=16 and SI1=28, we solve for R, then use SI1=100P×R×1 to find the principal P.
For 2 years, CI−SI=P(100R)2
Simple interest is constant per year, while compound interest increases due to reinvestment.
The extra interest of ₹16 is generated strictly from the ₹28 interest earned in the first year.
Using the difference formula significantly reduces calculation time in exams.
Formula-based methods can be prone to errors if the time period is not exactly 2 years.
Banking sector for loan interest calculations.
Financial planning and investment growth analysis.
Given SI=56 for 2 years, SI for 1 year = 28.
Difference = 72−56=16.
Using P=4×DiffSI2 is a common shortcut for 2-year problems.
Option B (42) and D (44) are common distractor values resulting from arithmetic errors.
C is correct — The principal is calculated as ₹49 by analyzing the growth difference between compound and simple interest over two years.
Always divide the simple interest by the number of years first to find the base interest per year, as this is the building block for both types of interest.
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