Question

Bakul brrowed ₹5000 from a finance company at 8%p.a.compound half-yearly. what amount of money will discharge his debt after 1year?​

Answer 1

AnswEr :

• Principal = Rs. 5000
• Compounded Half Yearly, Means Rate will be half and Year will be twice.
• Rate = 8% p.a. = 4% half yearly
• Time = 1 Year = 2 half yearly

• Let's head to the Question Now :

$\longrightarrow \sf{Amount = P \times \bigg(1 + \dfrac{r}{100} \bigg)^{t}}$

$\longrightarrow \sf{Amount = 5000 \times \bigg(1 + \cancel\dfrac{4}{100} \bigg)^{2}}$

$\longrightarrow \sf{Amount = 5000 \times \bigg(1 + \dfrac{1}{25} \bigg)^{2}}$

$\longrightarrow \sf{Amount = 5000 \times \bigg(\dfrac{25 + 1}{25} \bigg)^{2}}$

$\longrightarrow \sf{Amount = 5000 \times \bigg(\dfrac{26}{25} \bigg)^{2}}$

$\longrightarrow \sf{Amount = \cancel{5000}\times \dfrac{676}{\cancel{625}}}$

$\longrightarrow \sf{Amount =8 \times 676}$

$\longrightarrow \boxed{\sf{Amount =Rs.\: 5408}}$

⠀

∴ He will give Rs.5408 to discharge debt.

Answer 2

Given :---

• Principal = Rs.5000
• Rate = 8% p.a
• Time = 1 yr.
• Rate is compounded Half - Yearly

$\LARGE\bold\star\underline{\underline\textbf{Formula\:used}}$ ::---

• $\tiny\red{\boxed{\sf A\:=\:P( 1 + \frac{r}{100})^{t}}}$
• Time = 2×1 = 2 years.
• Rate = 8/2 = 4% .

$\Large\underline{\underline{\sf{Solution}:}}$

Putting values we get,,

$A = 5000(1 + \frac{4}{100} )^{2} \\ \\ \implies \: A = 5000( \frac{26}{25})^{2} \\ \\ \implies \: A = 5000 \times \frac{676}{625} \\ \\ \implies \: A = 5408$

Hence , we get, $\red{\bold{</strong><strong>Rs.5408</strong><strong>}}$ as amount After one year...