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 ?
Answer & explanation
Correct answer: option 4
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