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?

Answer 1

Answer:

28,756

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