Question

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)

plzz solve this sum with proper explanation I WILL MARK YOU AS BRAINLIST​

Answer 1

Answer:

The amount is Rs.28746.72.

Step-by-step explanation:

Given : 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.

To find : How much did he receive?

Solution :

Deposited on 6 Months and received on 10 Years.

Interest earned for 114 months =$19\times 6$Months

Deposited on 12 Months and received on 10 Years

Interest earned for 108 months = $18\times 6$ Months

Deposited on 8 Years (96 months) Received on 10 Years

Interest earned for  24 months = $4\times 6$ Months

Amount Deposited every time = Rs 1000

Rate of interest = 10 % PA = 5% for 6 months

The amount became,

$A=1000\times (1.05^{19} + 1.05^{18} + ......................+ 1.05^4)$

$A=1000\times 1.05^4(1+1.05+...........+1.05^{14}+1.05^{15})$

$A=1000\times 1.05^4(\frac{1.05^{16}-1}{1.05-1})$

$A=1000\times 1.05^4(\frac{2.1829-1}{0.05})$

$A=1000\times 1.05^4(23.65)$

$A=28746.72$

Therefore, The amount is Rs.28746.72.

Answer 2

28,756 Amount would be received at end of 10 Years

Step-by-step explanation:

Deposited on 6 Months   Received on 10 Years

interest earned for  114 months = 19 * 6 Months

Deposited on 12 Months Received on 10 Years

interest earned for  108 months = 18 * 6 Months

Deposited on 8 Years (96 months) Received on 10 Years

interest earned for  24 months = 4 * 6 Months

Amount Deposited every time = Rs 1000

Rate of interest = 10 % PA = 5% for 6 months

Amount  = 1000 * (  1.05¹⁹ + 1.05¹⁸ + ............................................+ 1.05⁴)

= 1000 * 1.05⁴(1 + 1.05 +....................................................+ 1.05¹⁴ + 1.05¹⁵)

= 1000 * 1.05⁴ ( 1.05¹⁶ - 1)/(1.05 - 1)

= 1000 * 1.05⁴ (2.1829 - 1)/(0.05)

= 28,756

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