Question

What sum will become rupees 9826 in 18 months if the rate of interest is 5/2% per annum and the interest is compounded Half-Yearly. ​

Answer 1

Answer:

Rs 9466.54

Explanation:

Let the required sum be P

We have :

$\star \sf \: Principal = P$

$\star \sf \: Amount = Rs \: 9826$

$\star \sf \: Rate \: = \dfrac{5}{2}\%$

$\star \sf \: Time = \dfrac{3}{2} \: years$

$\therefore \sf \: A = P(1 + \dfrac{r}{200} ) ^{2n}$

$\implies \sf \: 9826 = P(1 + \frac{ \frac{5}{2} }{200} ) ^{2 \times \frac{3}{2} }$

$\implies \sf \: 9826 = P(1 + \dfrac{1}{80} ) ^{3}$

$\implies \sf \:9826 = P(\dfrac{81}{80})^{3}$

$\implies \sf\: P = 9826\: \times (\dfrac{80}{81})^{3}$

$\implies \sf \: \: P = 9466.54$

Hence, Required sum = Rs 9466.54

Procedure Used :

We know that When interest is compounded Half-Yearly we have to Divide Rate by 2 and multiple the time by 2.

In case of Half-Yearly we have :

• Principal = P

• Rate = R/2% per half-year

• Time = 2n half-years.

$\therefore \sf \: Amount = P(1+\dfrac{r}{200})^{2n}$

Answer 2

||✪✪ QUESTION ✪✪||

What sum will become rupees 9826 in 18 months if the rate of interest is 5/2% per annum and the interest is compounded Half-Yearly.

|| ★★ FORMULA AND CONCEPT USED ★★ ||

when The interest is compounded Annually :-

❁ A = P[1+ (R/100) ]^T

Now, it Has Two case :---

⓵ When rate is compounded Half-Yearly :- We know that Half yearly Means Half of a year, when we Multiply it with 2 we will get a year . So we can say that in this case :-

• Rate is Divided by 2.

• Time is Multiply by 2 . ( To make it a complete year).

❷ when rate is compunded Quarterly :-- Quarterly means 3 months , now when we multiply 3 months with 4 , we gets a complete year .. So, here we can say that :-

• Rate is Divided by 4 .

• Time is Multiply by 4. ( To make it a complete year).

|| ✰✰ ANSWER ✰✰ ||

we have given that, a sum of money become Rs.9826 , That means this is our Amount after Given time ..

So,

➳ Amount = 9826

➳ Rate = Half of (5/2 %) = (5/4) %

➳ Time = 2 times of 18 Months = 18*2 = 36 Months = 3 years . (As 12 Months = 1 year).

➳ Principal = Let P .

Putting all values in above Told formula we get ,,

➺ 9826 = P * [ 1 + (5/4)/100 ]³

➺ 9826 = P * [ 1 + (5/400) ]³

➺ 9826 = P * [ 1 + (1/80) ]³

➺ 9826 = P * [ 81/80 ]³

➺ P = (9826 * 80 * 80 *80) / (81 * 81 * 81)

➺ P = Rs.9466.54 (Approx).

Hence, we can say that, The Principal was Rs.9466.54 (Approx) in This Case.