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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 ...
Calculation for Amount Received by A's Son:

Step 1: Calculate the number of deposits made by A's son.

Total number of years = 8 – (6/12) = 7.5 years

Number of deposits = 7.5*2 = 15

Step 2: Calculate the future value of each deposit after 10 years.

Future value of each deposit = Rs. 1000 * (1 + (10/2)/100)^(2*10) = Rs. 3104.07

Step 3: Calculate the total future value of all deposits.

Total future value of all deposits = Rs. 3104.07 * 15 = Rs. 46,560.98

Step 4: Present the total future value to A's son on his 10th birthday.

Amount received by A's son = Rs. 46,560.98

Explanation:

The question asks us to calculate the amount that A's son received on his 10th birthday after depositing Rs. 1000 every six months for 7.5 years in a savings account that earns 10% interest compounded semi-annually.

To solve the problem, we need to calculate the future value of each deposit after 10 years and then add up these future values to get the total future value of all deposits. Finally, we present this total future value to A's son on his 10th birthday.

We can calculate the future value of each deposit using the formula:

Future value = Principal * (1 + (rate/compounding frequency))^(compounding frequency * time)

Here, the principal is Rs. 1000, the rate is 10%, the compounding frequency is semi-annually (i.e., 2 times a year), and the time is 10 years.

After plugging in the values, we get the future value of each deposit as Rs. 3104.07.

To calculate the total future value of all deposits, we simply multiply the future value of each deposit by the number of deposits (i.e., 15).

Therefore, the total future value of all deposits is Rs. 46,560.98.

Finally, we present this amount to A's son on his 10th birthday.
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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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