Question

in how many years will ₹4000 amount to 4630.50 at 5% per annum , compounded annually?

Answer 1

Formula = A = P ( 1 + r/100 )^t
Principal (P) = Rs. 4000
Amount (A) = Rs. 4630.5
Rate(R) = 5%
Let the time period (t) be t.
Then,
4630.5 = 4000 ( 1 + 5/100)^t
when we transpose 4000 to RHS,
4630.5/4000=(21/20)^t { by cancelling 105/100}
(21/20)^3=(21/20)^t
when the bases are same on both sides we cancel them and their powers remain there
3 = t
Therefore Time = 3 years

Answer 2

$\bold{\large{\underline{\underline{\sf{StEp\:by\:stEp\:explanation:}}}}}$

→Amount = Rs. 4630.50

→Principal = Rs. 4000

→Rate = 5% p.a.

→Time = ?

So, simply by using the fromula of Amount of CI we can find the answer

$\implies \tt{Amount = P \times \bigg(1 + \dfrac{r}{100} \bigg)^{t}}$

$\implies \tt{4630.50 = 4000 \times \bigg(1 + \dfrac{5}{100} \bigg)^{t}}$

$\implies\tt{\cancel\dfrac{46305}{10} = 4000 \times \bigg(1 + \cancel\dfrac{5}{100} \bigg)^{t}}$

$\implies \tt{\dfrac{9261}{2} = 4000 \times \bigg(1 + \dfrac{1}{20} \bigg)^{t}}$

$\implies \tt{\dfrac{9261}{2 \times 4000} = \bigg(\dfrac{20 + 1}{20} \bigg)^{t}}$

$\implies \tt{\dfrac{9261}{8000} = \bigg(\dfrac{21}{20} \bigg)^{t}}$

$\implies \tt{\bigg(\dfrac{21}{20} \bigg)^{3} = \bigg(\dfrac{21}{20} \bigg)^{t}}$

$\longrightarrow \boxed{\sf time = 3 \: yrs.}$

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