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Examoogle • User • info@examoogle.com • EE-2024-8821
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In how many years will a sum of ₹12,000 become ₹14,520 at a rate of 10% per annum on compound interest, compounded annually?
5
2
4
3
2
Notice the ratio PA=1200014520=12001452=100121. Since 100121=(1.1)2, and (1+0.1)=1.1, the power n must be 2.
Principal sum P = 12000, Amount A = 14520, Rate of interest r = 10% per annum, Compounded annually
A=P(1+100r)n
Notice the ratio PA=1200014520=12001452=100121. Since 100121=(1.1)2, and (1+0.1)=1.1, the power n must be 2.
Students often miscalculate the ratio or blindly use the logarithmic formula when simple powers are sufficient, leading to arithmetic errors.
Set up the compound interest formula
Using the formula for amount in compound interest where P=12000, A=14520, r=10, and n is the number of years:
14520=12000(1+10010)n
Simplify the equation
Divide both sides by 12000 to isolate the exponential term:
1200014520=(1.1)n⟹12001452=(1.1)n
Solve for n
Reducing the fraction gives 1.21. Since 1.21=(1.1)2, we equate the exponents:
(1.1)2=(1.1)n⟹n=2
Option B is correct because the principal amount 12000 grows to 14520 in exactly 2 years at a 10% rate.
This ratio-based approach is highly efficient for problems involving population growth or depreciation where the time period is unknown.
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