Question

Find the sum of money which will amount to $27783 in 3 years at 5% per annum, the interest being compounded annually

Answer 1

Answer:

Rs 24000

Step-by-step explanation:

$\sf \: Amount = Rs \: 27783$

$\sf \: Time = 3 \: years$

$\sf \: Rate \: = 5 \%$

$\textbf{\underline{\underline{To\:Find\:The\:Principal}}}$

Let Principal be P

$\sf \: Amount = P(1 + \dfrac{r}{100} )^{n}$

$\sf \: 27783 = P (1 + \cancel \dfrac{5}{100} ) ^{3}$

$\sf \: 27783 = P (1 + \dfrac{1}{20} ) ^{3}$

$\sf \: 27783 = P (\dfrac{20 + 1}{20} ) ^{3}$

$\sf \: 27783 = P \: \times \dfrac{21}{20} \times \dfrac{21}{20} \times \dfrac{21}{20}$

$\sf \: 27783 = \dfrac{9261}{8000} P$

$\dfrac{9261 \: P}{8000} = 27783$

$\sf \: P = \dfrac{27783 \times 8000}{ 9261}$

$\sf \: P = 3 \times 8000$

$\boxed{\boxed{Principal=\: Rs\:24000}}$

Answer 2

$\large\sf \underline{ \underline{ \: Solution \: : \: \: \: }}$

Given ,

Amount (A) = $ 27783

Rate (R) = 5 %

Number of years (n) = 3 years

We know that ,

$\huge{ \star} \: \: \large\fbox{ \fbox{ \sf \: Amount = P {(1 + \frac{R}{100} )}^{n} \: }}$

$\implies \sf 27783 =P {(1 + \frac{5}{100} )}^{3} \\ \\ \implies \sf 27783 = P {(1 + \frac{1}{20} )}^{3} \\ \\ \implies \sf 27783 = P { (\frac{20 + 1}{20}) }^{3} \\ \\ \implies \sf 27783 = P {( \frac{21}{20} )}^{3} \\ \\\implies \sf 27783 = P \times \frac{9261}{8000} \\ \\ \implies \sf P \times 9261= 27783 \times 8000 \\ \\\implies \sf P = \frac{222264000}{9261} \\ \\ \implies \sf P = 24000$

Hence , the required value of principal (P) is $ 24000