Respuesta :
Answer:
Rs 20000
Step-by-step explanation:
Let the sum is x.
The rate of interest, r=20%=0.2
Time, t=2 years.
Total amount after t years, [tex]A= x \left(1+\frac{r}{n}\right)^{tn}[/tex]
The value of n when compounded annually, n=1
So, the total amount,
[tex]A_1=x \left(1+\frac{0.2}{1}\right)^{2\times 1}=x(1.2)^2[/tex]
The compound interest when compounded annually,
[tex]I_1 =x(1.2)^2-x[/tex]
The value of n when compounded semi-annually, n=2
So, the total amount, [tex]A_2 = x \left(1+\frac{0.2}{2}\right)^{2\times 2}=x(1.1)^4[/tex]
The compound interest when compounded semi-annually,
[tex]I_2 =x(1.1)^4-x[/tex]
As the difference between the annual and semi-annual compound interest on x amount of money is Rs 482, so
[tex]I_2-I_1=482 \\\\(x(1.1)^4-x)-(x(1.2)^2-x)=482 \\\\x(1.1)^4-x(1.2)^2=482 \\\\x(1.1^4 - 1.2^2) = 482 \\\\x(0.0241) = 482 \\\\x=482/0.0241 \\\\[/tex]
x=20000
Hence, the sum is Rs 20000.
