A certain sum invested at compound interest, amounts to ₹19965 at 10% p.a. in 3 years. The same sum will amount to ₹x at the same rate in $2\frac{2}{5}$years. If the interest is compounded yearly in both the cases, what is the value of x ?

18876

 Formula that we used here is :-

Amount = P$(1 \;+\; \frac{R}{100})^t$

19965 = P [ 1 +  \(\frac{10}{100}\) ]³

P = 19965 × \(\frac{10}{11}\) × \(\frac{10}{11}\) × \(\frac{10}{11}\)

= 15000

Now,

ATQ,

Rate for \(\frac{2}{5}\) th of year = 10% × \(\frac{2}{5}\) = 4%

Amount = P$(1 \;+\; \frac{R}{100})^t$

 = 15000 [ 1 +  \(\frac{10}{100}\) ]² × [ 1 +  \(\frac{4}{100}\) ]

= 15000 × \(\frac{11}{10}\) × \(\frac{11}{10}\) × \(\frac{26}{25}\)

= 18876