Question

8. Meenal lends * 75,000 at C.I. for 3 years. If
the rate of interest for the first two years is
15% per year and for the third year it is 16%,
calculate the sum Meenal will get at the end
of the third year in s.i​

Answer 1

Answer :

₹115057.5

Explanation :

We know that, any amount calculated for respective years we use the formula :

$\sf \: Amount = p \bigg( 1 + \dfrac{r_1}{100} \bigg) \bigg(1 + \dfrac{r_2}{100} \bigg)$

Where, $\sf r_1 \: \& \: r_2$ are the rate of first 2 years respectively.

Here, the sum of 75,000 is to be calculated for 3 years at the rate of 15% for the first 2 years and 16% for the 3rd year.

∴ Calculating the amount for 3rd year by,

$\sf \: Amount = p \bigg( 1 + \dfrac{r_1}{100} \bigg) \bigg(1 + \dfrac{r_2}{100} \bigg)\bigg(1 + \dfrac{r_3}{100}\bigg)$

Where,

• p(principal) = 75,000
• $\sf r_1 \: \& \: r_2$ = 15%
• $\sf r_3$ = 16%

By the given values,

$\sf \longrightarrow \: 75000 \bigg(1 + \dfrac{15}{100} \bigg)\bigg(1 + \dfrac{15}{100} \bigg)\bigg(1 + \dfrac{16}{100} \bigg)$

$\sf \longrightarrow \: 75000\bigg(1 + \dfrac{3}{20} \bigg)\bigg(1 + \dfrac{3}{20} \bigg)\bigg(1 + \dfrac{4}{25} \bigg)$

$\sf \longrightarrow \: 75000\bigg( \frac{23}{20} \bigg)\bigg( \frac{23}{20} \bigg)\bigg( \frac{29}{25} \bigg)$

$\sf \longrightarrow 115057.5$

∴ Amount for the 3rd year is ₹115057.5

Answer 2

$\small\tt\red{Interest\;for\;the\;first\:year\;}$

$\tt\red{\implies{ \frac{P\times R \times T}{100} }}$

$\tt\red{\implies{ \frac{75,000 \times 15 \times 1}{100} }}$ $\tt\red{=Rs.\;11,250}$

$\small\tt\red{Amount\;of\;first\;year}$

$\small\tt\red{\implies\;Rs.\;75,000+Rs.\;3,000=Rs.\;86,250}$

$\tt\red{Interest\;for\;the\; second\:year\;}$

$\tt\red{\implies{ \frac{P\times R \times T}{100} }}$

$\tt\red{\implies{ \frac{86,250\times 15 \times 1}{100} }}$ $\tt\red{=Rs.\;12,937.5}$

$\tt\red{Amount\;of\; second\;year}$

$\small\tt\red{\implies\;Rs.\;86,250+Rs.\;12,937.5=Rs.\;99,187.5}$

$\tt\red{Interest\;for\;the\; third\:year\;}$

$\tt\red{\implies{ \frac{P\times R \times T}{100} }}$

$\tt\red{\implies{ \frac{99,187.5\times 15 \times 1}{100} }}$ $\tt\red{=Rs.\;15,870}$

$\tt\red{Amount\;of\; third\;year}$

$\small\tt\red{\implies\;Rs.\;99,187.5+Rs.\;15,870=Rs.\;1,115,057.5}$

Hence, the sum meenal.will get at the end third year is Rs.1,115,057.5

Happy Learning :D