Question

A sum of money invested at 8% P.A. amounts to 12122 in 2 years . What will it amount to in 2 years 8 months at 9% P.A.

Answer 1

Step-by-step explanation:

Given:-

• A sum of money invested at 8% P.A. amounts to 12122 in 2 years.

To Find:-

• Amount in 2 years 8 months at 9% P.A.

Solution:-

Let the Principal be P

Given, Amount = Rs. 12122

$\rm Simple \: Interest = \dfrac{P \times T \times R}{100}$

Here:-

• T = 2 years, R = 8% , Principal = P

$\rm\dashrightarrow Amount = Simple\: Interest + Principal$

$\rm \implies 12122 = \dfrac{P \times T \times R}{100} + P$

$\rm \implies 12122 = \dfrac{P \times 2 \times 8}{100} + P$

$\rm \implies 12122 = \dfrac{16P}{100} + P$

$\rm \implies \dfrac{16P+100P}{100} = 12122$

$\rm \implies \dfrac{116P}{100} = 12122$

$\rm \implies P = 12122 \times \dfrac{100}{116}$

$\rm \implies P = 10450$

$\rm\therefore\underline{\: \: \underline{\: \: \pink{ Principal = Rs. 10450}\: }\: \:}$

Now, let us find the Amount in 2 years 8 months and rate 9%

$\rm Time = 2\: years \: 8 months = 2\dfrac{2}{3} = \dfrac{8}{3} \: years$

$\rm \implies SI = \dfrac{PTR}{100}$

$\rm \implies SI = \dfrac{ 10450 \times \dfrac{8}{3} \times 9}{100}$

$\rm \implies SI = Rs. 2508$

$\rm Now, \: Amount = SI + Principal$

$\rm = 2508 + 10450$

$\rm = 12958$

$\underline{\boxed{\purple{\rm \therefore Amount = Rs.12958}}}$