Question

At what rate per cent compound interest, 800 amounts to 926.10 in 1 ,1/2 years, interest being
compounded half yearly?​

Answer 1

$\bf \red{ \underline{ \underline{given}}}$

• principal, P= Rs 800
• Amount, A = Rs 926.10
• Time, n = 1 ½ = 3 half years
• Rate =r °/• p.a = r/2 per half year

$\bf \red{ \underline{ \underline{to \: find \: out}}}$

Rate of interest =?

$\bf \red{ \underline{ \underline{formula \: used}}}$

$\orange{A = p(1 + \frac{r}{100} ) {}^{n} }$

$\bf \red{ \underline{ \underline{solution}}}$

$A = p(1 + \frac{r}{100} ) {}^{n}$

$\star \: putting \: the \: value$

$= > 926.10 = 800(1 + \frac{r}{200} ) {}^{3}$

$= > \frac{926.10}{800} = (1 + \frac{r}{200} ) {}^{3}$

$= > \frac{9261}{8000} = (1 + \frac{r}{200} ) {}^{3}$

$= > ( \frac{21}{20} ) {}^{3 } = (1 + \frac{r}{200} ) {}^{3}$

$= > \frac{21}{20} = 1 + \frac{r}{200}$

$= > \frac{r}{200} = \frac{21}{20} - 1$

$= > \frac{r}{200} = \frac{1}{20}$

$= > r = \frac{200}{20}$

$= > \purple {r = 10}$

$\therefore \: \: required \: rate \: of \: interest \: is\: 10\%p.a$

Answer 2

Question:

At what rate per cent compound interest, 800 amounts to 926.10 in 1 ,1/2 years, interest being compounded half yearly?

Answer:

• The required interest rate is 10%.

Given:

• Principle = Rs. 800
• Amount = Rs.926.10
• Time period 1 and $\mathsf {\frac{1}{2}}$ = 3 half yearly

To Find:

• Rate of Interest = ?

Explanation:

$\underline\mathsf \red{Formula\:used\:here\: :-}$

• $\mathsf {A = P( 1 + \frac{R}{100})^n}$

Let 'R' be the rate of interest.

$\underline\mathsf\red {Now\: :-}$

$\mathsf {A = P( 1 + \frac{R}{100})^n}$

$:\implies \mathsf {926.10 = 800(1 + \frac{R}{200})^3}$

$:\implies \mathsf {\frac{926.10}{800} = (1 + \frac{R}{200})^3}$

$:\implies \mathsf {\frac{9261}{8000} = (1 + \frac{R}{200})^3}$

$:\implies \mathsf {(\frac{21}{20})^3 = (1 + \frac{R}{200})^3 }$

$:\implies \mathsf {\frac{21}{20} = 1+ \frac{R}{200}}$

$:\implies \mathsf {\frac{R}{200} = \frac{21}{20} - 1}$

$:\implies \mathsf {\frac{R}{200} = \frac{1}{20}}$

$:\implies \mathsf {R = \frac{200}{20} }$

$\therefore \mathsf {R = 10\%}$

• Hence, the required interest rate is 10%.