If the semi-annual compound interest of Rs15625 for 1 year 6 months is

1.	If the semi-annual compound interest of Rs15625 for 1 year 6 months is Rs 1951, find the rate of interest.
Answer» Given: The semi-annual COMPOUND INTEREST of Rs. 15625 for 1 year 6 months is Rs. 1951 To find: The rate of interest Solution: To SOLVE the given problem we will use the FOLLOWING formula of HALF-yearly compound interest: $\boxed{\bold{A = P [1 + \frac{\frac{R}{2}}{100} ]^2^n}}\\\\\boxed{\bold{C.I. = A - P}}$ Here we have C.I. = Rs. 1951 P = Rs. 15625 n = $1\frac{6}{12} = 1\frac{1}{2} = \frac{3}{2} \:years$ Now, using the above two formulas, we get $C.I. = P [1 + \frac{\frac{R}{2}}{100} ]^2^n - P$ substituting the given values $\implies 1951 = 15625 [1 + \frac{\frac{R}{2}}{100} ]^2^(^\frac{3}{2}^ ) - 15625$ $\implies 1951 + 15625 = 15625 [1 + \frac{\frac{R}{2}}{100} ]^3$ $\implies 17575 = 15625 [1 + \frac{R}{200} ]^3$ $\implies \frac{17575}{15625} = [1 + \frac{R}{200} ]^3$ taking cube roots on both sides $\implies \sqrt[3]{\frac{17575}{15625}} = \sqrt[3]{[1 + \frac{R}{200} ]^3}$ $\implies {\frac{26}{25} = [1 + \frac{R}{200} ]$ $\implies {\frac{26}{25} - 1 = \frac{R}{200}$ $\implies {\frac{26-25}{25} = \frac{R}{200}$ $\implies {\frac{1}{25} = \frac{R}{200}$ $\implies R = \frac{200}{25}$ $\implies \bold{R = 8\%}$ Thus, the rate of interest is → 8%. --------------------------------------------------------------------------------- Also View: What will be the compound interest on 5,000, if it is compounded half-yearly for 1 year 6 months at 8% per annum? brainly.in/question/12296626 What will Rs.80,000 amount to in 2 years at the rate of 20% p.a., if interest is compounded half yearly? brainly.in/question/12159582 Principal= ₹ 2560 Rate = 25/2% Time = 1 Year calculate the amount and C.I. if the interest is compounded half yearly. brainly.in/question/13435421