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. An amount is deposited in a bank of 10% rate of interest, compounded annually. it at the end of three years the interest amount is Rs. 2,648, then find the amount invested :
Answer (Detailed Solution Below)Option 2 : Rs. 8,000 Free RBI Assistant Prelims Full Mock Test 100 Questions 100 Marks 60 Mins Given: An amount is deposited in a bank of 10% rate of interest, compounded annually. it at the end of three years the interest amount is Rs. 2,648 Formula Used: C.I = P[( 1 + r/100)n - 1 ] C.I = compound interest, r = rate p.a., P = principal amount, n = time period or number of years Calculation: Let the amount deposited in the bank be Rs. 'P' ⇒ P[( 1 + 10/100)3 - 1] = 2648 ⇒ P × 331/1000 = 2648 ⇒ P = Rs. 8,000. ∴ The amount deposited in the bank is Rs. 8,000 Latest RBI Assistant Updates Last updated on Sep 21, 2022 The RBI (Reserve Bank of India) has released the list of finally selected candidates for the Jammu Region. The result is out for the 2021 recruitment cycle. A total of 950 vacancies were released under the recruitment process for RBI Assistant 2022. The selection of the candidates for the Assistant post consists of the Prelims exam, Mains exam, and Language Proficiency Test. Candidates who get a successful selection for RBI Assistant 2022 will get a salary range between Rs. 20700 to Rs. 55700. Check out RBI Assistant result here. Ace your Interest preparations for Compound Interest with us and master Quantitative Aptitude for your exams. Learn today! What will be the amount when 10000 is deposited in a bank at 10% per annum?Expert-verified answer
= 11297.5346 Rs ≈ 11300 Rs.
What will be the amount when 10000 is deposited in a bank at 10% per annum compounded annually for 2 years?= Rs. (10824.32 - 10000) = Rs. 824.32.
What is the compound amount of 10000 for 3 years at 10% compounded semi annually?Thus, The compound Interest will be Rs. 3310 .
What is the compound interest on rupees 10000 at 10% for 3 years?∴ Compound interest = ₹13860 – ₹10000 = ₹3860.
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