Question

What sum of money will amount to ₹7986 in 3 years at 10% per annum compound interest?

Answer 1

\Large A = P \left(1+\frac{r}{100}\right)^{n} => 7986 = 6000 \left(1+\frac{10}{100}\right)^{n} \)

=> \( \Large \frac{7986}{6000}=\frac{11}{10}^{n} => \frac{1331}{1000}= \left(\frac{11}{10}\right)^{n} => n = 3 years \)

Answer 2

Answer:

₹6,000

Explanation:

Let's say that, ₹$\boldsymbol x$ will amount to ₹7986 in 3 years at 10% p.a.(per annum) at compound interest.

Then,

By amount formula :

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

Where,

• Amount = 7986
• p(principal) = $\boldsymbol x$
• r(rate) = 10%
• n(time) = 3 years.

So,

$\sf \implies \: 7986 = \boldsymbol{x} \bigg(1 + \dfrac{10}{100} \bigg)^{3}$

$\sf \implies \: 7986 = \boldsymbol{x} \bigg(1 + \dfrac{1}{10} \bigg)^{3}$

$\sf \implies \: 7986 = \boldsymbol{x} \bigg(\dfrac{11}{10} \bigg)^{3}$

$\sf \implies \: 7986 = \boldsymbol{x} \bigg(\dfrac{1331}{1000} \bigg)$

$\sf \implies \: \dfrac{7986 \times 1000}{1331} = \boldsymbol{x}$

$\sf \therefore \: \boldsymbol{x} = 6000$

∴ The sum of the amount is ₹6,000

_____________________

Formula used :

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

Where,

• ‘p’ denotes the principal
• ‘r’ denotes the rate of interest.
• And, ‘n’ denotes number the time.