Question

Har Prasad saves evey year Rs. 3000, and invests it at the end of the year at 15% compound interest. Find the amount of his savings at the end of the fourth year is [3000(1+3/20)^(3)+3000(1+3/20)^(2)+3000(1+3/20)^(1)+3000] nearly.

Answer 1

He saves \Rs 3000 every year.
Consider the Rs 3000 that he saved at end of 1st year.
Rate of interest = 15% compound = 15/100 = 3/20
After 1 year amount becomes 3000+ 3/20 (3000) = 3000(1+3/20)
After 2 years amount becomes [3000(1+3/20)]+3/20[3000(1+3/20)]
= (1+3/20)[3000(1+3/20)]=3000(1+3/20)^2]
After 3 years the amoubnt becomes [3000(1+3/20)^2]+3/20[3000(1+3/20)^2
= (1+3/20)[3000(1+3/20)^2]=3000(1+3/20)^3]
So amount saved in 1st year becomes 3000(1+3/20)^3 after 3 years, that is, at end of 4th year.
Similarly amount saved in 2nd year (which uis also Rs 3000)becomes 3000[(1+3/20)^2] after 2
years, that is at end of 4th year
Similarly amount saved in 3rd year (which uis also Rs 3000) becomes 3000[(1+3/20)^1] after 1
year, that is at end of 4th year
Finally amount saved asfter 4 years remains Rs 3000 as it earns no interest until end of 4th year
Hence total mount after end of 4 years
= 3000(1+3/20)^3+3000[(1+3/20)^2] +3000[(1+3/20)^1]+3000
If you want the value it is 14980.12 Rs

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