Compound Interest: The future value (FV) of an investment of present value (PV) dollars earning interest at an annual rate of r compounded m times per year for a period of t years is: Show
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FV = PV(1 + r/m)mtor FV = PV(1 + i)n where i = r/m is the interest per compounding period and n = mt is the number of compounding periods. One may solve for the present value PV to obtain: PV = FV/(1 + r/m)mt Numerical Example: For 4-year investment of $20,000 earning 8.5% per year, with interest re-invested each month, the future value is FV = PV(1 + r/m)mt = 20,000(1 + 0.085/12)(12)(4) = $28,065.30 Notice that the interest earned is $28,065.30 - $20,000 = $8,065.30 -- considerably more than the corresponding simple interest. Effective Interest Rate: If money is invested at an annual rate r, compounded m times per year, the effective interest rate is: reff = (1 + r/m)m - 1. This is the interest rate that would give the same yield if compounded only once per year. In this context r is also called the nominal rate, and is often denoted as rnom. Numerical Example: A CD paying 9.8% compounded monthly has a nominal rate of rnom = 0.098, and an effective rate of: r eff =(1 + rnom /m)m = (1 + 0.098/12)12 - 1 = 0.1025. Thus, we get an effective interest rate of 10.25%, since the compounding makes the CD paying 9.8% compounded monthly really pay 10.25% interest over the course of the year. Mortgage Payments Components: Let where P = principal, r = interest rate per period, n = number of periods, k = number of payments, R = monthly payment, and D = debt balance after K payments, then R = P � r / [1 - (1 + r)-n] andD = P � (1 + r)k - R � [(1 + r)k - 1)/r] Accelerating Mortgage Payments Components: Suppose one decides to pay more than the monthly payment, the question is how many months will it take until the mortgage is paid off? The answer is, the rounded-up, where: n = log[x / (x � P � r)] / log (1 + r) Future Value (FV) of an Annuity Components: Ler where R = payment, r = rate of interest, and n = number of payments, then FV = [ R(1 + r)n - 1 ] / r Future Value for an Increasing Annuity: It is an increasing annuity is an investment that is earning interest, and into which regular payments of a fixed amount are made. Suppose one makes a payment of R at the end of each compounding period into an investment with a present value of PV, paying interest at an annual rate of r compounded m times per year, then the future value after t years will be FV = PV(1 + i)n + [ R ( (1 + i)n - 1 ) ] / i where i = r/m is the interest paid each period and n = m � t is the total number of periods. Numerical Example: You deposit $100 per month into an account that now contains $5,000 and earns 5% interest per year compounded monthly. After 10 years, the amount of money in the account is: FV = PV(1 + i)n + [ R(1 + i)n - 1 ] / i = Value of a Bond: V is the sum of the value of the dividends and the final payment. You may like to perform some sensitivity analysis for the "what-if" scenarios by entering different numerical value(s), to make your "good" strategic decision.
Replace the existing numerical example, with your own case-information, and then click one the Calculate. Find the compound interest on Rs. 20000 at 20 percent per annum for 12 months, compounded half yearly.
Answer (Detailed Solution Below)Option 3 : Rs. 4200 Free CT 1: Growth and Development - 1 10 Questions 10 Marks 10 Mins Given: Principal = Rs. 20000, Rate = 10 % per half-year, Time = 1 years = 2 half- years Formula: Amount = P (1 + (R/2)/100)2n Calculations: Amount = 20000 [1 + 10/100]2 Amount = Rs. 24,200 Compound Interest = Total amount – Principal ⇒ 24,200 – 20000 ⇒ Rs.4200 ∴ The required answer is Rs 4200. Last updated on Sep 21, 2022 The NCTE (National Council for Teacher Education) has revised the TET eligibility criteria recently and has issued a notification stating that a candidate who has been admitted or undergoing any of the Teacher Training Courses (TTC) is eligible for appearing in the TET Examination. Candidates appearing for the CTET (Central Teacher Eligibility Test) are exempted from any age limit. They have to just satisfy the required educational qualification. Candidates are qualified for the CTET exam based on their results in the written exam. The written exam will consist of Paper 1 and Paper 2 in which candidates have to score a minimum of 60% marks to qualify. Check out the CTET Selection Process here. Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now! What is the compound interest on Rs 20000 at 5% per annum for 2 years?I=10020000×2×5=Rs. 2,000. What is the compound interest of rupees 15000 for 2 years at 5% per annum?15000 at 5% per annum for two years is Rs 1500 and the amount after 2 years is Rs. 16500. What is the compound interest on rupees 20000 at 5% for 4 years?Hence, compound interest on Rs. 20,000 for 4 years at 5% p.a. is Rs. 4,310.125. What is the 5% interest of 20000?5 percent of 20000 is 1000. What will be the amount of 20000 after 2 years when the interest is compounded annually at the rate of 10% per annum also calculate the compound interest?4200. Was this answer helpful?
What is the compound interest on rupees 20000 at 5% for 4 years?Hence, compound interest on Rs. 20,000 for 4 years at 5% p.a. is Rs. 4,310.125.
What is the compound interest on rupees 20000 at 10% for 2 years?Where P is principal, R is rate of interest and T is time. ∴ The compound interest for 2 years is Rs. 2464.
What will be the compound interest on rupees 20000 at the rate of 5% per annum for 2 years?I=10020000×2×5=Rs. 2,000.
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Find the amount and the compound interest on Rs 20000 at 4 annum compounded annually after 2 years
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