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Six months’ intervals A deposited of Rs. 1000 in a savings account which credit interest at 10% p.a., compounded semi-annually. The first deposit was made when A’s son was 6 months old and last deposit was made when his son was 8 years old. The money remained in the account and was presented to the son on his 10th birthday. How much did he receive? (1.06)16 = 2.1829) (a) Rs.25740 (b) Rs.23740 (c) Rs.25860 (d) Rs.2576?
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Six months’ intervals A deposited of Rs. 1000 in a savings account whi...
Understanding the Problem
A deposited Rs. 1000 every six months starting when his son was 6 months old, until his son was 8 years old. The interest rate is 10% per annum, compounded semi-annually. The total amount will be calculated when the son turns 10.
Timeline of Deposits
- First deposit at 0.5 years (6 months)
- Last deposit at 8 years (or 16 deposits)
- Total duration for the last deposit until the son turns 10 years is 2 years (4 periods of 6 months)
Calculating Total Deposits
- Total deposits made: 16 (from 0.5 years to 8 years)
- Each deposit is Rs. 1000.
Calculating Compound Interest for Each Deposit
- The formula for compound interest is: A = P(1 + r/n)^(nt)
- Here, P = Rs. 1000, r = 0.10, n = 2 (since it's compounded semi-annually), and t = number of years until the son turns 10.
Periods for Each Deposit
- 1st deposit: 9.5 years (19 periods)
- 2nd deposit: 9 years (18 periods)
- ...
- 15th deposit: 1 year (2 periods)
- 16th deposit: 0.5 years (1 period)
Calculating Each Deposit's Future Value
- Future value for each deposit is calculated based on the number of compounding periods remaining until the son turns 10.
Summing Up All Future Values
- 1st deposit: 1000 * (1 + 0.05)^(19) = 1000 * 2.1829 = Rs. 2182.90
- 2nd deposit: 1000 * (1 + 0.05)^(18) = Rs. 2076.89
- ...
- 16th deposit: 1000 * (1 + 0.05)^(1) = Rs. 1050
Total Amount Received
- After calculating all future values and summing them up, A's son receives approximately Rs. 25740.
Conclusion
Thus, the total amount A’s son receives on his 10th birthday is Rs. 25740.
Answer: (a) Rs. 25740
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Six months’ intervals A deposited of Rs. 1000 in a savings account which credit interest at 10% p.a., compounded semi-annually. The first deposit was made when A’s son was 6 months old and last deposit was made when his son was 8 years old. The money remained in the account and was presented to the son on his 10th birthday. How much did he receive? (1.06)16 = 2.1829) (a) Rs.25740 (b) Rs.23740 (c) Rs.25860 (d) Rs.2576?
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Six months’ intervals A deposited of Rs. 1000 in a savings account which credit interest at 10% p.a., compounded semi-annually. The first deposit was made when A’s son was 6 months old and last deposit was made when his son was 8 years old. The money remained in the account and was presented to the son on his 10th birthday. How much did he receive? (1.06)16 = 2.1829) (a) Rs.25740 (b) Rs.23740 (c) Rs.25860 (d) Rs.2576? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Six months’ intervals A deposited of Rs. 1000 in a savings account which credit interest at 10% p.a., compounded semi-annually. The first deposit was made when A’s son was 6 months old and last deposit was made when his son was 8 years old. The money remained in the account and was presented to the son on his 10th birthday. How much did he receive? (1.06)16 = 2.1829) (a) Rs.25740 (b) Rs.23740 (c) Rs.25860 (d) Rs.2576? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Six months’ intervals A deposited of Rs. 1000 in a savings account which credit interest at 10% p.a., compounded semi-annually. The first deposit was made when A’s son was 6 months old and last deposit was made when his son was 8 years old. The money remained in the account and was presented to the son on his 10th birthday. How much did he receive? (1.06)16 = 2.1829) (a) Rs.25740 (b) Rs.23740 (c) Rs.25860 (d) Rs.2576?.
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