Question

9. A sum of money is invested at a half-yearly compound interest rate of 5%. If the difference of
principals at the ends of 6 months and 12 months be Rs 126 then find
(i) the sum of money invested, and
(ü) the amount at the end of 1! years.​

Answer 1

(i) The sum of money invested = RS 4032.

(ii) The amount at the end of first year = RS 4326.12.          

To find:

(i) The sum of money invested ?

(ii) The amount at the end of first year ?

Given data:

Rate of interest = 5%

Difference between the principle at the end of 6 months and 12 months = RS.126

Formula:

CI = $\text{P}(1+\frac{\text{r}}{100})^\text{n}$

$\text{x}+\text{y}+\frac{\text{xy}}{100}$

Solution:

Rate of interest = 5%

Since calculated half-yearly, rate of interest for 6 months = 2.5%

Difference between the principle at the end of 6 months and 12 months = RS 126

Difference between the rate of interest at the end of 6 months and 12 months is calculated as,

                     $[\text{x}+\text{y}+\frac{\text{xy}}{100}] - [\text{x}+\text{y}+\frac{\text{xy}}{100}]$

                  = $[2.5+2.5+\frac{2.5\times2.5}{100}]-[2.5]$

                 = 5.625 - 2.5

                 = 3.125

Thus 3.125 = 126

Then 100 = ?

                = $\frac{126\times100}{3.125}$

                = 4032.

Therefore,

(i) The sum of money invested = RS 4032

(ii) The amount at the end of first year,  

CI = $4032(1+\frac{2.5}{100} )^2$

    = $4032(\frac{102.5}{100} )^2$

    = $4032(1.025)^2$

    = 4032 × 1.050625

CI = 4326.12

                                                                                                                      

To solve more:

1. A sum rupees 25000 invested at 8% per annum compounded semi annually amount to 28121.60.Find the time period.

https://brainly.in/question/2572033

2. Find simple interest on ₹1300 at the rate of 5% per annum for 146 days

https://brainly.in/question/1567778

Answer 2

Answer:

Let the principal be P.

Rate of interest per half year = 5%

Amount at the end of 6 months = P(1 + 5/100)

Amount at the end of 1 year = P(1 + 5/100)2

Difference between the amounts = Rs 126 P(1 + 5/100)2 - P(1 + 5/100)

= 126 P(21/20)2 - P(21/20)

= 126 P(441/400) - P(21/20)

= 126 (441P - 420P) / 400

= 126 21P/400 = 126

P = 2400

So, the sum of money invested is Rs 2400

Amount at the end of 1 and half year = 2400(1 + 5/100)3

= 2400 (21/20)3

= 2400 (9261/8000)

= Rs 2778.30