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Imagine you put $ 100 in a savings account with a yearly interest rate of 6 % . After one year, you have 100 + 6 = $ 106 . After two years, if the interest is simple , you will have 106 + 6 = $ 112 (adding 6 % of the original principal amount each year.) But if it is compound interest , then in the second year you will earn 6 % of the new amount: 1.06 × $ 106 = $ 112.36 Yearly Compound Interest FormulaIf you put P dollars in a savings account with an annual interest rate r , and the interest is compounded yearly, then the amount A you have after t years is given by the formula: A = P ( 1 + r ) t Example: Suppose you invest $ 4000 at 7 % interest, compounded yearly. Find the amount you have after 5 years. Here, P = 4000 , r = 0.07 , and t = 5 . Substituting the values in the formula, we get: A = 4000 ( 1 + 0.07 ) 5 ≈ 4000 ( 1.40255 ) = 5610.2 Therefore, the amount after 5 years would be about $ 5610.20 . General Compound Interest FormulaIf interest is compounded more frequently than once a year, you get an even better deal. In this case you have to divide the interest rate by the number of periods of compounding. If you invest P dollars at an annual interest rate r , compounded n times a year, then the amount A you have after t years is given by the formula: A = P ( 1 + r n ) n t Example: Suppose you invest $ 1000 at 9 % interest, compounded monthly. Find the amount you have after 18 months. Here P = 1000 , r = 0.09 , n = 12 , and t = 1.5 (since 18 months = one and a half years). Substituting the values, we get: A = 1000 ( 1 + 0.09 12 ) 12 ( 1.5 ) ≈ 1000 ( 1.143960 ) = 1143.960 Rounding to the nearest cent, you have $ 1143.96 . What will be the compound interest on Rs 4000 in two years when rate of interest is 5% per annum? SolutionWe know that amount A at the end of n years at the rate of R % per annum is given by A = P\[ \left( 1 + \frac{R}{100} \right)^n . \] Answer Verified
Hint: First we’ll find the compound interest for 2 years by using its formula. Rest of the 2 months’ interest will be simple because it’s given that the compound interest will be applied annually. In the end, we’ll add both the interest and subtract from the principal amount.Complete step by step solution: Hence, option (c) is the correct option. Note: Students usually make mistakes in such a type of problem where for some time period compound interest is applied and for some time period, simple interest is applied. It’s always recommended from our side to read the question carefully, especially the interest section. Whether the interest is applied monthly or annually also of which kind, simple of the compound. What will be the compound interest on 4000 at 6% per annum for 2 and half years?∴ Compound interest is Rs. 410.
What will be the compound interest on 4000 for 2 years at the rate of 5% per annum?So, the correct answer is “410 Rs.”.
What is the compound interest on Rs 4000 at 10 per annum for 2 years and 3 months compounded annually?4961∴ C.I. = A - P = Rs. 4961 - 4000=Rs. 961 (c)
What will be the compound interest on a principal of rupees 4000 for 2 year when the rate of interest is 15% per annum?∴ Compound interest for 2 years = Rs. 200 + Rs. 210 = Rs. 410.
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