Practice Questions
Concept Explanation
When interest is compounded half-yearly, the annual rate is halved and the number of periods is doubled.
Key Formula
A = P(1 + R/200)^(2T)
- Rate per half-year = R/2
- Number of periods = 2T
Example
P = Rs. 10,000, R = 10%, T = 1 year. A = 10000 × (1.05)^2 = Rs. 11,025.
-
Q1 EasyIf interest is compounded half-yearly, find CI on Rs. 8000 at 10% p.a. for 1 year.ExplanationRate per half-year = 5%; periods = 2. A = 8000 × (1.05)^2 = 8000 × 1.1025 = Rs. 8,820. CI = 8820 − 8000 = Rs. 820. Answer: C.
-
Q2 EasyThe compound interest on Rs. 16,000 at 10% per annum for 1 year, compounded half-yearly, is:ExplanationA = 16000 × (1.05)^2 = 16000 × 1.1025 = Rs. 17,640. CI = 17640 − 16000 = Rs. 1,640. Answer: C.
-
Q3 EasyAmount on Rs. 10,000 at 10% for 1 year compounded half-yearly is:ExplanationA = 10000 × (1.05)^2 = Rs. 11,025. Answer: B.
-
Q4 EasyAmount on Rs. 5,000 at 20% for 1 year compounded half-yearly is:ExplanationRate per half-year = 10%. A = 5000 × (1.10)^2 = 5000 × 1.21 = Rs. 6,050. Answer: B.
-
Q5 EasyFor half-yearly compounding at 10% p.a., the rate applied each half-year is:ExplanationHalf-yearly rate = R/2 = 10/2 = 5% per half-year. Answer: B.
-
Q6 MediumFind the compound interest on Rs. 2500 for 2 years at 4% per annum compounded half-yearly.ExplanationRate per half-year = 2%; periods = 4. A = 2500 × (1.02)^4 = 2500 × 1.08243216 = Rs. 2,706.08. CI = 2706.08 − 2500 = Rs. 206.08. Answer: C.
-
Q7 MediumThe effective annual rate corresponding to a nominal rate of 8% p.a. compounded half-yearly is:ExplanationEffective rate = (1.04)^2 − 1 = 1.0816 − 1 = 0.0816 = 8.16%. Answer: C.
-
Q8 MediumCI on Rs. 10,000 at 10% for 1 year (half-yearly) exceeds the SI by:ExplanationCI = 10000 × (1.05)^2 − 10000 = Rs. 1,025. SI = Rs. 1,000. Excess = 1025 − 1000 = Rs. 25. Answer: C.
-
Q9 MediumAmount on Rs. 15,000 at 12% for 1 year compounded half-yearly is:ExplanationRate per half-year = 6%. A = 15000 × (1.06)^2 = 15000 × 1.1236 = Rs. 16,854. Answer: B.
-
Q10 MediumAmount on Rs. 8,000 at 8% for 1 year compounded half-yearly is approximately:ExplanationA = 8000 × (1.04)^2 = 8000 × 1.0816 = Rs. 8,652.80 ≈ Rs. 8,653. Answer: C.
-
Q11 HardThe effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:ExplanationHalf-yearly rate = 6/2 = 3%. Effective annual rate = (1 + 3/100)^2 − 1 = (1.03)^2 − 1 = 1.0609 − 1 = 0.0609 = 6.09%. Answer: D.
-
Q12 HardA bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:ExplanationRate per half-year = 5/2 = 2.5%. January deposit grows for 2 half-years: 1600 × (1.025)^2 = Rs. 1,681. July deposit grows for 1 half-year: 1600 × 1.025 = Rs. 1,640. Total amount = 1681 + 1640 = Rs. 3,321. Interest gained = 3321 − 3200 = Rs. 121. Answer: B.
-
Q13 HardWhat is the difference between the compound interests on Rs. 5000 for 1.5 years at 4% per annum compounded yearly and half-yearly?ExplanationYearly (1.5 years): A = 5000 × 1.04 × (1 + 0.04 × 1/2) = 5000 × 1.04 × 1.02 = Rs. 5,304; CI = Rs. 304. Half-yearly: 3 periods at 2%; A = 5000 × (1.02)^3 = Rs. 5,306.04; CI = Rs. 306.04. Difference = 306.04 − 304 = Rs. 2.04. Answer: A.
-
Q14 HardA customer deposits Rs. 2,000 on 1st January and Rs. 2,000 on 1st July in a bank offering 4% p.a. compounded half-yearly. Interest earned by year-end is:ExplanationRate per half-year = 2%. First deposit: 2000 × (1.02)^2 = Rs. 2,080.80. Second: 2000 × 1.02 = Rs. 2,040. Interest = 2080.80 + 2040 − 4000 = Rs. 120.80. Answer: B.
-
DS1 Easy
What is the compound interest for 1 year?
Statement IPrincipal is Rs. 8,000 at 10% p.a.
Statement IIInterest is compounded half-yearly.
ExplanationTogether: A = 8000 × (1.05)^2 = Rs. 8,820; CI = Rs. 820. Neither alone fixes the compounding frequency and all of P, R, T. Answer: C. -
DS2 Medium
What is the effective annual rate?
Statement INominal rate is 6% per annum.
Statement IIInterest is payable half-yearly.
ExplanationTogether: effective rate = (1.03)^2 − 1 = 6.09%. Both are needed. Answer: C.
-
DS3 Hard
What is the interest gained in one year?
Statement IA bank gives 5% p.a. compounded half-yearly; Rs. 1,600 is deposited on 1st January and again on 1st July.
Statement IIEach deposit earns interest at 2.5% per half-year for the remaining half-years of that year.
ExplanationStatement I alone has P, R and deposit dates → interest = Rs. 121 as in the classic problem. Statement II alone lacks the deposit amount. Answer: A. -
DS4 Hard
What is the difference between yearly and half-yearly CI for 1.5 years?
Statement IP = Rs. 5,000 and R = 4% per annum.
Statement IICompounding frequencies compared are yearly and half-yearly.
ExplanationTogether: yearly CI = Rs. 304, half-yearly CI = Rs. 306.04, difference = Rs. 2.04. Both needed. Answer: C.