a father desire to distribute 51783 amongst his two sons who are respectively 12 and 15 years olds in such a way that the sums invested @5% p.a. compound interest will give the same amount to both of them when they attain the age of 18. how should he divide the sum
Answers
I hope this answer will clear ur all doubts .
Solution :-
Case 1) :- (younger son.)
→ Principal = Let Rs.x
→ Time = 18 - 12 = 6 years.
→ Rate = 5% PA compounded annually .
→ Amount = P[1 + (R/100)]^Time
Putting all values we get,
→ Amount at the age of 18 = x[1 + (5/100)]⁶
→ Amount at the age of 18 = x[1 + (1/20)]⁶
→ Amount at the age of 18 = x(21/20)⁶
Case 2) :- (Elder son.)
→ Principal = Rs.(51783 - x)
→ Time = 18 - 15 = 3 years.
→ Rate = 5% PA compounded annually .
→ Amount = P[1 + (R/100)]^Time
Putting all values we get,
→ Amount at the age of 18 = (51783 - x)[1 + (5/100)]³
→ Amount at the age of 18 = (51783 - x)[1 + (1/20)]³
→ Amount at the age of 18 = (51783 - x)(21/20)³
Now, we have given that, at the age of 18, both will get same amount .
Therefore,
→ x * (21/20)⁶ = (51783 - x)(21/20)³
→ (51783 - x) / x = (21/20)⁶ ÷ (21/20)³
→ (51783 - x) / x = (21/20)^ (6 - 3)
→ (51783 - x) / x = (21/20)³
→ (51783 - x) / x = (9261/8000)
→ 51783 * 8000 - 8000x = 9261x
→ 9261x + 8000x = 51783 * 8000
→ 17261x = 51783 * 8000
→ x = Rs.24,000 .
Hence,
→ Elder son gets = 51783 - 24000 = Rs.27,783 .
So, Younger son gets Rs.24,000 and Elder son gets Rs.27,783.
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