Question

31. What amount is to be repaid on a loan of Rs 40,000 for 2 years at 20 % per annum compounded half
yearly?​

Answer 1

As A total amount = P(1+r/n)^nt where r=R/100 and n is how many times compounded annually

Answer 2

Step-by-step explanation:

✦ Given :

• Amount of ₹40,000 is to be repaid after 2 years at 20% p. a. (per annum) compounded half-yearly.

✦ To find :

• Find out the amount will be added in these 2 years.

✦ Using the formula :

${ \underline{ \boxed{ \sf{amount = \bigg(1 + \frac{r}{100} \bigg) ^n}}}}$

$\begin{gathered} { \textsf { \textbf{Here}}} \begin{cases} \sf{p(principal) = 40000} \\ \sf{r\%(rate\%) = 10\%(compounded \: half \: yearly)} \\ \sf{n(time) = 4years(compounded \: half-yearly} \\ \end{cases} \end{gathered}$

✦ From the given values :

$\sf \longrightarrow Amount = 40000\bigg(1 + \frac{10}{100} \bigg)^{4}$

$\sf \longrightarrow Amount = 40000 \bigg( \frac{110}{100} \bigg)^{4}$

$\sf \longrightarrow Amount = 40000 \times \frac{110}{100} \times \frac{110}{100} \times \frac{110}{100} \times \frac{110}{100}$

$\sf \longrightarrow Amount = 40,000 \times 1.1 \times 1.1 \times 1.1 \times 1.1$

$\sf \longrightarrow Amount = 40,000 \times (1.1)^4$

$\sf \longrightarrow Amount = 40,000 \times 1.4641$

$\sf \longrightarrow Amount = 58,564$

Therefore the amount to be repaid after 2 years is ₹58,564 ☑