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At 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)?
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At six months’ intervals A deposited of Rs. 1000 in a savings account ...
Solution:
Given:
Principal amount (P) = Rs.1000
Rate of interest (r) = 10% p.a.
Compounding period (n) = 2
Time period (t) = 16 half years (8 years = 16 half years)
Calculation:
1. Calculation of interest for each deposit:
Amount = P(1 + r/n)^(n*t)
Amount = 1000(1 + 0.1/2)^(2*0.5)
Amount = Rs. 1102.50
Interest = Amount - P
Interest = Rs. 102.50
2. Calculation of total amount after all deposits:
Since the deposits are made at six-month intervals, there will be 2 deposits every year. Thus, total number of deposits made = 2*8 = 16
Total amount after all deposits = Rs. 1000 + 16*102.50
Total amount after all deposits = Rs. 2600
3. Calculation of final amount at the end of 10 years:
Final amount = 2600(1 + 0.1/2)^(2*6)
Final amount = Rs. 4403.84
4. Calculation of amount received by son:
The final amount is presented to the son on his 10th birthday, which is 16 half years after the first deposit was made. Thus, the final amount will be further compounded for 16 half years.
Amount received by son = 4403.84(1 + 0.1/2)^(2*16)
Amount received by son = Rs. 8026.85
Explanation:
The interest is compounded semi-annually, which means that interest is added to the principal amount after every 6 months. The formula for calculating the amount after n periods of compounding is A = P(1 + r/n)^(n*t), where A is the final amount, P is the principal amount, r is the rate of interest, n is the number of compounding periods per year, and t is the total number of years.
In this question, the principal amount is Rs. 1000, the rate of interest is 10% p.a., and the compounding period is 2 (semi-annually). The first deposit is made when the son is 6 months old and the last deposit is made when the son is 8 years old. The total time period is 8 years, which is equivalent to 16 half years.
Thus, we calculate the amount after each deposit using the formula A = P(1 + r/n)^(n*t). After all the deposits are made, the total amount is calculated by adding up the amount after each deposit. Finally, the total amount is compounded for the remaining 16 half years to get the amount received by the son on his 10th birthday.
Given:
Principal amount (P) = Rs.1000
Rate of interest (r) = 10% p.a.
Compounding period (n) = 2
Time period (t) = 16 half years (8 years = 16 half years)
Calculation:
1. Calculation of interest for each deposit:
Amount = P(1 + r/n)^(n*t)
Amount = 1000(1 + 0.1/2)^(2*0.5)
Amount = Rs. 1102.50
Interest = Amount - P
Interest = Rs. 102.50
2. Calculation of total amount after all deposits:
Since the deposits are made at six-month intervals, there will be 2 deposits every year. Thus, total number of deposits made = 2*8 = 16
Total amount after all deposits = Rs. 1000 + 16*102.50
Total amount after all deposits = Rs. 2600
3. Calculation of final amount at the end of 10 years:
Final amount = 2600(1 + 0.1/2)^(2*6)
Final amount = Rs. 4403.84
4. Calculation of amount received by son:
The final amount is presented to the son on his 10th birthday, which is 16 half years after the first deposit was made. Thus, the final amount will be further compounded for 16 half years.
Amount received by son = 4403.84(1 + 0.1/2)^(2*16)
Amount received by son = Rs. 8026.85
Explanation:
The interest is compounded semi-annually, which means that interest is added to the principal amount after every 6 months. The formula for calculating the amount after n periods of compounding is A = P(1 + r/n)^(n*t), where A is the final amount, P is the principal amount, r is the rate of interest, n is the number of compounding periods per year, and t is the total number of years.
In this question, the principal amount is Rs. 1000, the rate of interest is 10% p.a., and the compounding period is 2 (semi-annually). The first deposit is made when the son is 6 months old and the last deposit is made when the son is 8 years old. The total time period is 8 years, which is equivalent to 16 half years.
Thus, we calculate the amount after each deposit using the formula A = P(1 + r/n)^(n*t). After all the deposits are made, the total amount is calculated by adding up the amount after each deposit. Finally, the total amount is compounded for the remaining 16 half years to get the amount received by the son on his 10th birthday.
Community Answer
At six months’ intervals A deposited of Rs. 1000 in a savings account ...
1000 × (1.05)^16 -1 / 0.05 =
23657.49 + 5% + 5% +5% +5% = 28755.82
=28756
23657.49 + 5% + 5% +5% +5% = 28755.82
=28756
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At 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)?
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At 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)? 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 At 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)? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At 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)?.
At 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)? 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 At 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)? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At 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)?.
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