Question

what sum of money will amount to rs.9,260 in three years at the rate of 5% per annum if the interest is compounded annually?​

Answer 1

To Find :-

The Principal or the sum of money.

Given :-

• Amount = Rs. 9260

• Time = 3 years

• Rate of interest = 5% p.a.

We know :-

⠀⠀⠀⠀⠀⠀⠀⠀⠀Amount Formula :-

$\boxed{\underline{\bf{A = P\bigg(1 + \dfrac{R}{100}\bigg)^{n}}}}$

Where :-

• A = Amount
• R = Rate of interest
• n = Time Period
• P = Principal

Solution :-

By using the Amount Formula and substituting the values in it, we get :-

$:\implies \bf{A = P\bigg(1 + \dfrac{R}{100}\bigg)^{n}} \\ \\ \\ \\ :\implies \bf{9260 = P\bigg(1 + \dfrac{5}{100}\bigg)^{3}} \\ \\ \\ \\ :\implies \bf{9260 = P\bigg(\dfrac{100 + 5}{100}\bigg)^{3}} \\ \\ \\ \\ :\implies \bf{9260 = P\bigg(\dfrac{105}{100}\bigg)^{3}} \\ \\ \\ \\ :\implies \bf{9260 = P\bigg(\dfrac{21}{20}\bigg)^{3}} \\ \\ \\ \\ :\implies \bf{9260 = P \times \dfrac{21}{20} \times \dfrac{21}{20} \times \dfrac{21}{20}} \\ \\ \\ \\ :\implies \bf{9260 = P \times \dfrac{9261}{8000}} \\ \\ \\ \\ :\implies \bf{\dfrac{1}{P} = \dfrac{\dfrac{9261}{8000}}{9260}} \\ \\ \\ \\ :\implies \bf{\dfrac{1}{P} = \dfrac{1.16}{9260}} \\ \\ \\ \\ :\implies \bf{P = \dfrac{9260}{1.16}} \\ \\ \\ \\ :\implies \bf{\dfrac{1}{P} = 7982.76} \\ \\ \\ \therefore \purple{\bf{P = 7982.76}}$

Hence, the principal or thr sum of money is Rs. 7982.76.