Question

At what rate percent per annum CI will Rs 2000 amounts to Rs 2315.25 in 3 years.

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

Given That :-

→ Principal = P = Rs.2000

→ Time = T = 3 Years.

→ Amount = A = Rs.2315.25

→ Rate = R = Let R% .

Putting All values in formula we get :-

→ A = P [ 1 + (R/100) ]^T

→ 2315.25 = 2000 * [ 1 + (R/100) ]³

→ (231525/200000) = [ 1 + (R/100) ]³

→ (25 * 9261) / (25 * 8000) = [ 1 + (R/100) ]³

→ (9261/8000) = [ 1 + (R/100) ]³

→ (21/20)³ = [ 1 + (R/100) ]³

→ [ 1 + (1/20)]³ = [ 1 + (R/100) ]³

→ [ 1 + (5/100)]³ = [ 1 + (R/100) ]³

Comparing Now, we get,

☛ Rate = R% = 5% (Ans.)

Answer 2

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

• Principal = 2000Rs
• Amount = 2315.25
• Time = 3 years

${\bf{\blue{\underline{To \:Find:}}}}$

• Rate =?

${\bf{\blue{\underline{Fomula\:Used:}}}}$

$\dagger \: \: \: {\sf{ A = P\bigg(1 + \frac{R}{100} \bigg) ^{t} }}$

${\bf{\blue{\underline{Now:}}}}$

$: \implies \: {\sf{ 2315.25= 2000 \bigg(1 + \frac{r}{100} \bigg) ^{3} }}$

$: \implies \: {\sf{ \frac{2315.25}{2000} = \bigg(1 + \frac{r}{100} \bigg) ^{3} }}$

$: \implies \: {\sf{ \frac{2315.25}{2000} = \bigg(1 + \frac{r}{100} \bigg) ^{3} }}$

$: \implies \: {\sf{ \frac{231525}{200000} = \bigg(1 + \frac{r}{100} \bigg) ^{3} }}$

$: \implies \: {\sf{ \frac{9261}{8000} = \bigg(1 + \frac{r}{100} \bigg) ^{3} }}$

$: \implies \: {\sf{ \bigg(\frac{21}{20} \bigg) ^{3} = \bigg(1 + \frac{r}{100} \bigg) ^{3} }}$

If exponent are equal bases will also be equal,

$: \implies{\sf{ \frac{21}{20} = 1 + \frac{R}{100} }}$

$: \implies{\sf{ \frac{R}{100} = \frac{21}{20} - 1}}$

$: \implies{\sf{ \frac{R}{100} = \frac{21 - 20}{20} }}$

$: \implies{\sf{ \frac{R}{100} = \frac{1}{20} }}$

$: \implies{\sf{ R = \frac{1}{20} \times 100}}$

$: \implies{\sf{ R = 5\%}}$

$\dagger \: \: \boxed{\sf { Rate \: of \: interest = 5\%}}$