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
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) 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 ) ] / 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. Q.1.The difference in simple interest and compound interest on a certain sum of money in 2 years at 10 % p.a. is Rs. 50. The sum is a) Rs. 10000 b) Rs. 6000 c) Rs. 5000 d) Rs. 2000 e) None of these Q.2. The difference in simple interest and compound interest on a certain sum of money in 2 years at 18 % p.a. is Rs. 162. The sum is a) Rs. 4000 b) Rs. 5200 c) Rs. 4250 d) Rs. 5000 e) None of these Q.3. The compound interest on a certain sum of money for 2 years is Rs. 208 and the simple interest for the same time at the same rate is Rs. 200. Find the rate %.
 a) 5 % b) 6 % c) 7 % d) 4 % e) 8 % Q.4.The difference between compound interest and simple interest on a certain sum for 2 years at 10 % is Rs. 25. The sum is a) Rs. 1200 b) Rs. 2500 c) Rs. 750 d) Rs. 1250 e) Rs. 2000 Q.5.The simple interest on a certain sum for 3 years in Rs. 225 and the compound interest on the same sum for 2 years is Rs. 165. Find the rate percent per annum. a) 20 % b) 2.5 % c) 5 % d) 15 % e) 7.5% Q.6.The simple interest on a sum of money for 2 years is Rs. 150 and the compound interest on the same sum at same rate for 2 years is Rs. 155. The rate % p.a. is a) 16 % b) 20/3 % c) 12 % d) 10 % e) None of these Q7.Mihir’s capital is 5/4 times more than Tulsi’s capital. Tulsi invested her capital at 50 % per annum for 3 years (compounded annually). At what rate % p.a. simple interest should Mihir invest his capital so that after 3 years, they both have the same amount of capital? a) 20/3 % b) 10 % c) 50/3 % d) 1.728 % e) None of these Q8.The difference in simple interest and compound interest on a certain sum of money in 3 years at 10 % p.a. is Rs. 372. The sum is a) Rs. 8000 b) Rs.9000 c) Rs. 10000 d) Rs. 12000 e) None of these Q9.Sahil’s capital is 1/6 times more than Chaya’s capital. Chaya invested her capital at 20 % per annum for 2 years (compounded annually). At what rate % p.a. simple interest should Sahil invest his capital so that after 2 years, they both have the same amount of capital? a) 10% b) 11 5/7% c) 20% d) 13 5/7% e) None of these Q10.The difference in simple interest and compound interest on a certain sum of money in 3 years at 20 % p.a. is Rs. 640. The sum is
a) Rs. 5000 b) Rs. 8500 c) Rs. 8250 d) Rs. 6000 e) None of these What's the difference between the compound interest and the simple interest on a sum of Rs 9000 for 2 years at 5% per?Detailed Solution. ∴ The difference between S.I. and C.I. for 2 years is Rs. 44.10.
What is the difference between the compound interest and simple interest on Rs 8000?Amount=P(1+r100)n=8000(1+5100)2=8000×(1+120)2=8000×(2120)2=8000×441400=20×441=8820∴CI=Amount−Principal=8820−8000=820. Q. A person invests Rs. 5,000 for three years at a certain rate of interest compounded annually.
What is the difference between the compound interest and simple interest for the sum of?The difference between compound interest and simple interest on a sum for 3 years at 5% per annum is Rs. 122.
What is the difference between simple interest and compound interest on Rs 1000 at 10% for 5 years?Answer: Principal sum = ₹1000, interest rate = 10%p.a. , time= 4yrs. Simple interest= P.R.T/100 = 1000×10×4/100 = 400. Compound interest= P{1+ R/100}™ - P =1000{1+10/1000}^4-1000 = 1464.1 - 1000 = 464.1 Thus difference in interests= 464.1 - 400 = ₹64.1.
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Whats the difference between the compound interest and the simple interest on a sum of Rs 9000 for 2 years at 5% per?
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