Question

Naina borrowed some money from her friend for which she paid a simple interest of Rs 360 for 2 years. If the interest was compounded annually then she would have had to pay Rs 400 as interest for the same period. Calculate the money that was borrowed by Naine.​

Answer 1

Given: Naina borrowed some money from her friend for which she paid a simple interest of Rs 360 for 2 years. If the interest was compounded annually then she would have had to pay Rs 400 as interest for the same period.

To find: We have to find the principal.

Solution:

Let the principal be P and the rate of interest is r% per annum.

Naina borrowed some money from her friend for which she paid a simple interest of Rs 360 for 2 years.

So, simple interest will be-

$360 = p \times 2 \times \frac{r}{100} \\ \frac{r}{100} = \frac{180}{p}$

Given that the compound interest on the same principle is 400.

This compound interest will be-

$400 = p {(1 + \frac{r}{100} )}^{2} - p \\ 400 = p (1 + 2 \times \frac{r}{100} + \frac{ {r}^{2} }{100} ) - p\\ 400 = p(1 + 2 \times \frac{180}{p} + \frac{ {180}^{2} }{ {p}^{2} } ) - p\\400 = p + 360 + \frac{ {180}^{2} }{p} - p \\ 40 = \frac{32400}{p} \\ p = \frac{32400}{40} \\ p = 810$

So, the principle is 810 rupees.