Question

A sum of money amounts to ₹ 10240 in 2 years at 6 2/3% per annum, compounded annually. Find the sum. ​

Answer 1

Given:-

• $\sf{A = Rs.10240}$
• $\sf{T = 2\:years}$
• $\sf{R = 6\dfrac{2}{3}\% = \dfrac{20}{3}\%}$

To find:-

Sum of money

Solution:-

We know,

$\sf{A = P\bigg(1 + \dfrac{r}{100}\bigg)^t}$

= $\sf{10240 = P\bigg(1 + \dfrac{20}{\dfrac{3}{100}}\bigg)^2}$

= $\sf{10240 = P\bigg(\dfrac{100 + \dfrac{20}{3}}{100}\bigg)^2}$

= $\sf{10240 = P\bigg(\dfrac{300+ 20}{3}\times\dfrac{1}{100}\bigg)^2}$

= $\sf{10240 = P\bigg(\dfrac{320}{3}\times\dfrac{1}{100}\bigg)^2}$

= $\sf{10240 = P\bigg(\dfrac{320}{300}\bigg)^2}$

= $\sf{P = 10240\times \dfrac{300}{320}\times\dfrac{300}{320}}$

= $\sf{P = 9000}$

$\sf{\therefore The\:Sum\:of\:money\:is\:Rs.9000}$

From the solution:-

• A = Amount
• P = Principal
• T = Time
• R = Rate