Question : Rs. 6000 is lent at the rate of 8% per annum on compound interest (compounded quarterly). What will be the compound interest of 6 months?
Option 1: Rs. 268.60
Option 2: Rs. 190.50
Option 3: Rs. 164.60
Option 4: Rs. 242.40
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Correct Answer: Rs. 242.40
Solution : When compounded annually, where $A$ is the total amount, $P$ is the principal amount, $R$ is the rate of interest per annum (in decimal), and $T$ is the time in years. $\mathrm {A= P(1+\frac{R}{4})^{4T}}$ Given that: $P$ = Rs. 6000, $R$ = 8% = 0.08 and $T$ = 6 months = 0.5 years $\mathrm {A= 6000(1+\frac{0.08}{4})^{4 \times0.5}}\mathrm {= 6000(1.02)^{2}}=\mathrm { 6242.40}$ $\therefore$ Compound interest = A – P = 6242.40 – 6000 = Rs. 242.40 Hence, the correct answer is Rs. 242.40.
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Question : At what rate of compound interest per annum, a sum of Rs. 20,000 becomes Rs. 23,152.50 in 1 year and 6 months compounded half-yearly?
Option 1: 10% per annum
Option 2: 5% per annum
Option 3: 12% per annum
Option 4: 8% per annum
Question : What will be the compound interest on Rs. 21000 at the rate of 10% per annum for 6 months compounded half-yearly?
Option 1: Rs. 1680
Option 2: Rs. 1050
Option 3: Rs. 1850
Option 4: Rs. 1250
Question : In how many years will the simple interest on a sum of Rs. 6000 lent at 5% per annum be equal to the simple interest on a sum of Rs. 2000 lent for 30 years at 4% per annum?
Option 1: 6 years
Option 2: 12 years
Option 3: 20 years
Option 4: 8 years
Question : The difference between the simple interest and the compound interest at the same rate for INR 32,000 for 2 years is 80. What is the rate of interest, if in the case of compound interest, interest is compounded annually?
Option 1: 8% per annum
Option 2: 2% per annum
Option 3: 5% per annum
Option 4: 12% per annum
Question : A sum was lent for one year at the rate of 16 percent per annum on compound interest (compounding annually). If the compounding had been done half yearly, then the interest would have increased by Rs. 64. What was the sum lent?
Option 1: Rs. 10000
Option 2: Rs. 6000
Option 3: Rs. 14000
Option 4: Rs. 20000
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