A sum of Rs 40,000 at annual compound interest becomes Rs 56,169 in 2 years. What is the interest rate?
Divide the amount by the principal: 56,169/40,000 = 1.404225.
For 2 years, the annual growth factor squared is 1.404225. Taking the square root gives 1.185.
$Annual rate = (1.185 - 1) \times 100 = 18.5%$
A sum of money amounts to Rs 4,624 in 2 years and to Rs 4,913 in 3 years at a certain rate of interest, when interest is compounded per annum. The sum is:
The amount grows from ₹4,624 after 2 years to ₹4,913 after 3 years. The third-year interest is 4,913 - 4,624 = ₹289 .
Rate = 289/4,624 $\times 100 = 6.25%$. Thus, the annual growth factor is 1.0625 = 17/16.
Amount after 2 years = P $\times (17/16)² =$ ₹4,624 . Therefore, P = 4,624 $\times (16/17)² =$ ₹4,096
The difference between simple interest and compound interest, compounded annually, on a certain sum of money for 2 years at 16% per annum is Rs 797. Find the sum (rounded off to nearest integer).
For 2 years, the difference between CI and SI is P $\times (R/100)²$.
$Substitute R = 16%: 797 = P \times 0.16² = P \times 0.0256.$
$P = 797/0.0256 =$ ₹31,132.8125 . Rounded to the nearest rupee, $P =$ ₹31,133
A person borrows Rs 28,400 at 15% compound interest per year, compounded annually. At the end of every year, he pays Rs 9,100 as part payment. How much does he still owe after two such instalments?
Calculate the balance after the first year. ₹28,400 $\times 1.15 =$ ₹32,660 .
Subtract the first payment: ₹32,660 - ₹9,100 = ₹23,560 .
Apply one more year of 15% interest to the remaining balance: ₹23,560 $\times 1.15 =$ ₹27,094 .
Subtract the second payment: ₹27,094 - ₹9,100 = ₹17,994 still owed
A sum of ₹25,000 is invested at 12% per annum compound interest, compounded annually. What will be the difference between the compound interest and simple interest after 3 years?
Identify the given values.
Principal (P) = ₹25,000
Rate (R) = 12% per annum
Time (T) = 3 years
Calculate Simple Interest (SI).
SI = (P \times R \times T) / 100
SI = (25,000 \times 12 \times 3) / 100
SI = ₹9,000
Calculate Compound Interest (CI).
Amount = P \times (1 + R/100)^T
Amount = 25,000 \times (1.12)^3
Amount = 25,000 \times 1.404928
Amount = ₹35,123.20
CI = Amount - Principal
CI = 35,123.20 - 25,000
CI = ₹10,123.20
Find the difference.
Difference = CI - SI
Difference = 10,123.20 - 9,000
Difference = ₹1,123.20
( ₹1,123.20 )