Question

A man wishes to accumulate capital worth rs.50,4000 at the end of 3 years from now. if he can invest his savings at 5 per cent per annum compoundinterest, what equal sum must be put aside each year, beginning at the end of the first year, to obtain the required amount.

please give me the solution of this question ASAP

Answer 1

Suppose each year the man puts aside (saves) P amount of money.

At the end of 1st year the accumulated capital = P (1+ 5/100) = 1.05 P
At the end of 1st year he save an additional amount: P
So total amount of savings at the end of 1st year: P+1.05P = 2.05 P

At the end of 2nd year the accumulated capital : 2.05P(1+5/100) = 2.05 * 1.05 P
At the end of 2nd year he save an additional amount: P
So total amount of savings at the end of 2nd year: 2.1525P+P = 3.1525 P

At the end of 3nd year the accumulated capital : 3.1525P(1+5/100) = 3.310125 P
He puts aside an amount = P

Total amount = P+3.310125 P = 4.310125 P  = Rs 50,400

P = Rs 11,693.40
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Another way:
Accumulated capital = P(1+5/100)³ + P(1+5/100)²+P(1+5/100)+P
                               = 4.310125 P
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If the man does not add an amount P at the end of the 3rd year, then answer will be different:
3.310125 P = Rs 50,400
P = Rs 15,226

Answer 2

Let he aside sum of amount = x  
After one year he have total amount = $x(1 + 5/100) ^{1}$
= $1.05x$
He adds again his saving amount so, the total amount at starting of second year = $1.05x + x$
= $2.05x$
Again he got compound interest, so he has amount = $2.05x(1 + 5/100) ^{1}$
= $2.1525x$
Now he adds his saving , so he has total amount at the end of three year = 
$2.1525x + x$
= $3.1525x$
And given he has 50,440 at the end of three year , so
$3.1525x$ = $50,440$
$x$ = $16,000$
So he had set aside Rs 16,000 per year.