Question

a sum of money is invested at a half yearly compound interest rate of 5% if the difference of principal at the end of 6 month and 12th month be rupees 126 then find the sum of the money invested and the amount at the end of 3 upon 2 year​

Answer 1

Amount Deposited is Rs. 4919.07/-

Step-by-step explanation:

• Initially, staring with First $\frac {1}{2}$ year:

Let Rs. x be the Principal

And Rate, R = 5%

Time, T = $\frac {1}{2}$year

So, Interest = $\frac {Principal \times Rate \times Time}{100}$

= $\frac {x \times 5 \times 1}{2 \times 100} = Rs. \frac {x}{40}$

Now, After the end of 6 Months, amount becomes = Principal + Interest = $x + \frac {x}{40} = \frac {41x}{40}$

• For, Next 6 months,    

Principal = Rs. $\frac {41x}{40}$

And Rate, R = 5%

Time, T = $\frac {1}{2}$ year

Now,  

Interest = $\frac {Principal \times Rate \times Time}{100}$

= $\frac {41x \times 5 \times 1}{40 \times 2 \times 100}$

= Rs. $\frac {41x}{1600}$

After ending the next 6 month, Amount = $\frac {41x}{1600} + \frac {41x}{1600} = Rs. \frac {1681x}{1600}$

• For next slot or 3rd Half Year-

Principal = Rs. $\frac {1681x}{1600}$

And Rate, R = 5%

Time, T = $\frac {1}{2}$ year

Now,  

Interest = $\frac {Principal \times Rate \times Time}{100}$

= $\frac {1681x \times 5 \times 1}{1600 \times 2 \times 100} = Rs. \frac {1681}{64000}$

Amount = $\frac {1681}{64000} + \frac {1681}{64000} = Rs. \frac {68921x}{64000}$

Now,  

$\frac {1681x}{1600} - \frac {41x}{40}$ = 126  

or $\frac {41x}{1600}$ = 126

x = $\frac {126 \times 1600}{41}$ = 4917.07

• So, Money Invested or Principal Totals = Rs. 4917.07
• And, Finally the amount that would be received after 18 months (1.5 years) =  Rs. $\frac {68921x}{64000} \times \frac {126 \times 1600}{41}$ = Rs. 5295.15