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. 5-3 Future Value of an Annuity What is the future value of a $900 annuity payment over five years if interest rates are 8 percent? (LG5-2) 900 x [ (1+.08)^5 -1/.08] 900 x [1.5868/.08] 469.44 = 4224.96 5-5 Present Value Compute the present value of a $2,000 deposit in year 1 and another $1,500 deposit at the end of year 3 if interest rates are 10 percent. (LG5-3) 5-7 Present Value of an Annuity What's the present
value of a $900 annuity payment over five years if interest rates are 8 percent? (LG5-4) 5-11 Present Value of an Annuity Due If the present value of an ordinary, 7-year annuity is $6,500 and interest rates are 7.5 percent, what's the present value of the same annuity due? (LG5- 5-15 Effective Annual Rate A loan is offered with monthly payments and a 10 percent APR. What's the loan's effective annual rate (EAR)? (LG5-7 5-21 Present Value Given a 6 percent interest rate, compute the present value
of payments made in years 1, 2, 3, and 4 of $1,000, $1,200, $1,200, and $1,500. (LG5-3 5-39 Loan Payments You wish to buy a $25,000 car. The dealer offers you a 4-year loan with a 9 percent APR. What are the monthly payments? How would the payment differ if you paid interest only? What would the consequences of such a decision be? (LG5-9) Answer & Explanation Solved by verified expert <p>at, ultrices ac magna. Fusce dui lectus, congue vel laoreet ac, dictum vitae odio. Donec aliquet. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nam lacinia pulvinar tortor nec facilisis. Pellentes</p> Unlock full access to Course Hero Explore over 16 million step-by-step answers from our library Subscribe to view answer  docx What is the present value of a $900 annuity payment over five years if interest rates are 8 percent?Summary: The present value of a $900 annuity payment over five years if interest rates are 8 percent is $3600.
What is the future value of a $1000 annuity payment over five years if interest rates are 9 %?The future value of the annuity is $5,984.71.
What's the present value of a $800 annuity payment over six years if interest rates are 10 percent?Present value of the annuity is $3,933.86.
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What is the future value of a $900 annuity payment over five years if interest rates are 8 percent?
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