Question

10. A man invested Rs. 16,000 at compound interest for 3 years, interest compounded
annually. If he got Rs. 18522 at the end of 3 years, what is rate of interest?
(a) 10%
(b) 8%
(c) 5%
(d) 7%
​

Answer 1

Given :

• A man invested Rs. 16,000 at compound interest for 3 years, interest compounded
• annually. If he got Rs. 18522 at the end of 3 years.

To Find :

• Rate of interest = ?

Solution :

• Principal (P) = Rs. 16000
• Amount (A) = Rs. 18522
• Time (n) = 3 years

Let the rate of interest be 'r'.

Finding the rate of interest :

⋙ A = P(1 + r/100)ⁿ

⋙ 18522 = 16000(1 + r/100)³

⋙ 18522 ÷ 16000 = (1 + r/100)³

⋙ 9261 ÷ 8000 = (1 + r/100)³

⋙ (21/20)³ = (1 + r/100)³

⋙ (21/20) = 1 + r/100

⋙ (21/20) - 1 = r/100

⋙ 1/20 = r/100

⋙ 1/20 × 100 = r

⋙ 1/2 × 10 = r

⋙ 1 × 5 = r

⋙ r = 5 %

• Hence, the rate of interest is 5 %.

Answer 2

$\large{\boxed{\boxed{\sf Let's \: Understand \: Question \: F1^{st}}}}$

Here, we have said that a man invested the sum of ₹16,000 at a Compund Interest of 3yrs which is compounded annually. If after 3yrs he got ₹18522 the what will be the rate of interest.

$\large{\boxed{\boxed{\sf How \: To \: Do \: It?}}}$

Here, we simply use the formula (A = P[1+r/100]^t) and then substituting the given values in the formula we will find the rate which is our required answer.

Let's Do It ⚡

$\huge{\underline{\boxed{\sf AnSwer}}}$

____________________________

Given:-

• Principal, P = ₹16,000
• Time, t = 3yrs
• Amount, A = ₹18522

Find:-

• Rate of interest, r

Solution:-

Here, we know that

$\begin{lgathered}\\ :\implies\: \: \: \: \: \: \: \: \: \boxed{\sf A=P{\bigg\lgroup 1 + \dfrac{r}{100}\bigg\rgroup}^t}\\ \\ \end{lgathered}$

$\begin{lgathered} \\ \: \: \: \: \: \: \sf where \small{\begin{cases}\sf A = Rs.18522 \\ \sf P = Rs.16000 \\ \sf t = 3yrs \end{cases}} \\ \\ \end{lgathered}$

$\bigstar$ Substituting these values:

$\begin{lgathered}\\ \dashrightarrow\: \: \: \sf A=P{\bigg\lgroup 1 + \dfrac{r}{100}\bigg\rgroup}^t\\ \\ \dashrightarrow\: \sf 18522=16000{\bigg\lgroup 1 + \dfrac{r}{100}\bigg\rgroup}^3\\ \\\dashrightarrow\: \sf \dfrac{18522}{16000}= {\bigg\lgroup 1 + \dfrac{r}{100}\bigg\rgroup}^3\\ \\\dashrightarrow\: \sf \dfrac{9261}{8000}= {\bigg\lgroup 1 + \dfrac{r}{100}\bigg\rgroup}^3\\ \\\dashrightarrow\: \sf {\bigg\lgroup \dfrac{21}{20}\bigg\rgroup}^ {\not3}= {\bigg\lgroup 1 + \dfrac{r}{100}\bigg\rgroup}^{ \not3}\\ \\\dashrightarrow\: \sf \dfrac{21}{20}= 1 + \dfrac{r}{100}\\ \\\dashrightarrow\: \sf \dfrac{21}{20} - 1=\dfrac{r}{100}\\ \\\dashrightarrow\: \sf \dfrac{21 - 20}{20}= \dfrac{r}{100}\\ \\\dashrightarrow\: \sf \dfrac{1}{20}=\dfrac{r}{100}\\ \\\dashrightarrow\: \sf \dfrac{1}{20} \times 100=r\\ \\\dashrightarrow\: \sf 5\%=r\\ \\ \end{lgathered}$

$\begin{lgathered}\boxed{\sf \therefore The\:rate\:of\: Interest\:is\:5\%}\\\end{lgathered}$