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)
(a) Rs.25740
(b) Rs.23740
(c) Rs.25860
(d) Rs.25760
Answers
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
Answer: 28756
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