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?

₹38,115

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

------------------------------------------------------------

Overall                    2000       :    2541

ATQ,

2000R = 30000

1R = 15

Now, 2541R = 2541 × 15 = Rs.38115

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