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)

(a) Rs.25740

(b) Rs.23740

(c) Rs.25860

(d) Rs.25760

Answer is Rs.23740 can you explain it how ??

Answer 1

A deposited of Rs."1000" every 6 months from 6 month to 8 year will be 28756.45 rs after 10 years

Step-by-step explanation:

interest rate = 5% semi annually

1st deposit will earn interest for 19*6 month

last deposit will earn interest for 4 * 6 months

Amount received = 1000*(1.05)^4 + 1000*(1.05)^5 + .........+ 1000*(1.05)^19

= 1000*(1.05)^4( 1 + 1.05 + ...... +1.05^15)

= 1000 * 1.05^4 (1.05^16 - 1)/(1.05-1)

= 1000 * 1.05^4 (2.1829 - 1)/(0.05)

= 21000 * 1.05^3 * 1.1829

= 28756.45

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