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A certain sum of money is invested at the rate of 5% per annum compound interest,
the interest compounded annually. If the difference between the interests of third
year and first year is 102.50. Find the sum.
Answers
EXPERT VERIFIED ANSWER:-
→ Let Principal = P
→ Rate = 5% per annum compounded Annually .
→ Diff. b/w CI of 3rd year - CI of first year = Rs.102.5
First Year :-
→ Amount = P(1+R/100)^T
→ A = P(1 + 5/100)¹
→ A = P(1 + 0.05)
→ A = 1.05P
So,
→ CI of first year = Amount - Principal = 1.05P - P = 0.05P.
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Second Year :-
→ Amount = P(1+R/100)^T
→ A = P(1 + 5/100)²
→ A = P(1 + 0.05)²
→ A = (1.05)²P
→ A = 1.1025P
So,
→ CI of first year = Amount - Principal = 1.1025P - P = 0.1025P.
__________________
Third Year :-
→ Amount = P(1+R/100)^T
→ A = P(1 + 5/100)³
→ A = P(1 + 0.05)³
→ A = (1.05)³P
→ A = 1.157625P
So,
→ CI of first year = Amount - Principal = 1.157625P - P = 0.157625P
__________________
Now,
→ CI for third year = CI till third year-CI till second year
→ CI for third year = 0.157625P - 0.1025P = 0.055125P
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Therefore,
→ Diff. b/w 3rd year CI & 1st year CI = 0.055125P - 0.05P = 0.005125P.
__________________
Hence,
→ 0.005125P = 102.5
→ P = (102.5) ÷ (0.005125)
→ P = Rs.20,000 (Ans.)
Hence, The Required sum is Rs.20,000 .