Ali deposited $100 in a saving account at six months intervals, which credit interest at 10% per annum compounded semiannually. When Ali’s son was six months old, the first deposit was made. The money remained in the account and was given to the son on his 10th birthday. How much did he receive?
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Answer:
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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