The compound interest amounts on a certain sum at a certain rate percentage p.a. for the second year and third year are ₹3,300 and ₹3,630, respectively. What is the amount of the same sum at the same rate in $2\frac{1}{2}$ years, interest compounded yearly?
Answer & explanation
Correct answer: option 2
We know ,
Amount = Principal × ( 1 + \(\frac{rate }{100}\) )t
3630 = 3300 × ( 1 + \(\frac{rate }{100}\) )1
( 1 + \(\frac{rate }{100}\) ) = \(\frac{3630 }{3300}\)
\(\frac{rate }{100}\) = \(\frac{3630 }{3300}\) - 1
\(\frac{rate }{100}\) = \(\frac{330 }{3300}\)
rate = 10%
Now , Sum = 3300 × \(\frac{100 }{110}\) = 30000
CI for 1st year = 20% and CI for last \(\frac{1 }{2}\) year = \(\frac{10 }{2}\)%
= 5%
Principal : Amount
For 1st year 10 : 11
For 2nd year 10 : 11
For 0.5th year 20 : 21
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Overall 2000 : 2541
ATQ,
2000R = 30000
1R = 15
Now, 2541R = 2541 × 15 = Rs.38115
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