A certain sum amounts to Rs. 7350 in 2 years and to Rs. 8575 in 3 years when compounded annually. The sum and rate of interest is?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs. 5400 and 16.66 %
Under compound interest, the amount at the end of each year is the amount of the year before multiplied by \(\left(1+\frac{r}{100}\right)\). So the amount after 3 years divided by the amount after 2 years gives this factor, and the rate follows from it.
The rate (from the amounts of years 2 and 3):
The third year turns 7350 into 8575: \(\displaystyle 1+\frac{r}{100}=\frac{8575}{7350}=\frac{7}{6}\)
So the rate is \(\displaystyle r=\frac{100}{6}=16\frac{2}{3}\%=16.66\ldots\%\)
The sum (the amount after 2 years is the sum times the factor twice):
Amount after 2 years: \(\displaystyle P\times\left(\frac{7}{6}\right)^{2}=7350\)
So the sum is \(\displaystyle P=7350\times\frac{36}{49}=\) Rs. 5400