Question

Calculate the amount and the compound interest on:
Rs. 8,000 in 2.5 years at 15 percent per annum​

Answer 1

Concept:-

Here, We have to find Amount and Compound Interest on a Principal of ₹8,000 at 15% per annum for 2.5 years. We use certain formulas to find the Amount and Compound Interest.

Given:-

• Principal = ₹ 8,000
• Rate%  = 5% per annum
• Time = 2.5 years

To Find:-

• Amount
• Compound Interest

Solution:-

Here, Convert Time into fraction = 2 years 5 months

1 year = 12 months

$\sf{So,\ In\ fraction\ time\ =\ 2\dfrac{5}{12} \ years.}$

$\sf{Now,\ Amount = P\bigg(1 + \dfrac{R}{100}\bigg)^{T}\ for\ 2\ years,}$

Here, P = ₹ 8,000

         R = 15 %

         T = 2 years

$\sf{So, }$  $\sf{Amount = 8,000\bigg(1 + \dfrac{15}{100}\bigg)^{2}}$

⇒ $\sf{8,000\bigg(1 + \dfrac{3}{20}\bigg)^{2}}$

⇒ $\sf{8,000\bigg(\dfrac{20 + 3}{20}\bigg)^{2}}$

⇒ $\sf{8,000\bigg(\dfrac{23}{20}\bigg)^{2}}$

⇒ $\sf{8,000 \times \dfrac{23}{20} \times \dfrac{23}{20}}$

⇒ $\sf{20 \times 23 \times 23}$

⇒ $\sf{Rs.\ 10,580}$

$\sf{Now,\ Interest\ for\ \dfrac{5}{12}\ years\ on\ ₹\ 10,580\ at\ rate\ of\ 15\%,}$

⇒ $\sf{\dfrac{P \times R \times T}{100}}$

⇒ $\dfrac{10,580 \times 15 \times \dfrac{5}{12}}{100}$

⇒ $\sf{Rs.\ 661.25}$

$\sf{Total Amount =}$  $\rm{Rs.\ 10,580 + Rs.\ 661.25}$

                    $\sf{=}$  $\sf{Rs.\ 11,241.25}$

$\sf{Now,\ Compound\ Interest = Amount - Principal}$

                                      ⇒ $\sf{Rs.\ 11,241.25 - Rs.\ 8,000}$

                                      ⇒ $\sf{Rs.\ 3,241.25}$

$\sf{Hence,\ Amount\ =}$  $\sf{Rs.\ 11,241.25}$

$\sf{And,\ Compound\ Interest\ = }$  $\sf{Rs.\ 3,241.25}$