Find the Final amount of Rs 25000 at 9% p.a. in 3 years compounded half yearly
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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
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)mtNumerical 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) = $28,065.30Notice 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: 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) where Log is the logarithm in any base, say 10, or e.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 ) ] / iwhere 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: 5,000(1+0.05/12)120 + [100(1+0.05/12)120 - 1 ] / (0.05/12) = $23,763.28 Value of a Bond: Let N = number of year to maturity, I = the interest rate, D = the dividend, and F = the face-value at the end of N years, then the value of the bond is V, whereV = (D/i) + (F - D/i)/(1 + i)NV 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. MENU:Replace the existing numerical example, with your own case-information, and then click one the Calculate. Note: Simple interest is a fixed proportion of the principal amount borrowed or lent that is paid or received over a period of time. In the case of compound interest, interest is always higher than in the case of simple interest and the rate of formula is always given in fraction. Toc: Cover What will be the Compound Interest 25000 after 3 years at the rate 12 pa?(1+12100)3=25000(2825×2825×2825)=35123.20.
What will be the compound interest on Rs 25000 for 3 years at 6% per annum compounded annually?4775.
What will be the compound interest of 25000 for 3 years at 8% per annum compounded annually?Amount = ₹ 33264.
How much will Rs 25000 invested at compound interest amount to in 1 year at 4% per annum compounded half yearly?Detailed Solution
4,20,000/- to Rs. 4,80,000/-.
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