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 Rs.102.50 , find the sum.
Answers
Solution :-
→ 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.
__________________
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
__________________
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 .
Step-by-step explanation:
ANSWER
Let the sum (Principle) = Rs. 100
C.I. of 1st year = Rs. \frac{100\times 5\times 1}{100} = Rs. 5$$
And, amount of 1st year = Rs. 100 + Rs. 5=Rs. 105$$
⇒ The principke for 2nd year = Rs. 105
C.I. of 2nd year =Rs.
100
105×5×1
=Rs.5.25
And, amount of 2nd year =Rs.105+Rs.5.25=Rs.110.25
⇒ The principle for 3rd year =Rs.110.25
C.I. of 3rd year =Rs.
100
110×5×1
=Rs.5.5125
Difference between C.L of 1st year and C.L of 3rd year =Rs.5.5125−Rs.5=Rs.0.5125
Now, when the difference of interest =Rs.0.5125,sum=Rs.100
And, when the difference of interest =Rs.61.50,sum=Rs.
0.5125
100
×61.50=Rs.12,000