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?
(a) Rs.25740
(b) Rs.23740
(c) Rs.25860
(d) Rs.25760
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?
(b) Rs.23740
(c) Rs.25860
(d) Rs.25760
Ans
Hello student
so from the question it is given that the ,
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)
= 28786
Thanks and Regards ,
Harshit Tyagi
Hello student
so from the question it is given that the ,
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)
= 28786
Thanks and Regards ,
Harshit Tyagi