line‚ but we need to remember to apply different interest rates. The time line is: 0 1 Stock Bond $800 $350 360 361 ... 660 … $800 $350 $800 $350 $800 $350 $800 $350 C C C We need to find the annuity payment in retirement. Our retirement savings ends at the same time the retirement withdrawals begin‚ so the PV of the retirement withdrawals will be the FV of the retirement savings. So‚ we find the FV of the stock account and the FV of the bond
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Question 1 When you retire 40 years from now‚ you want to have $1.2 million. You think you can earn an average of 12 percent on your investment. To meet your goal‚ you are trying to decide whether to deposit lump sum today‚ or to wait and deposit a lump sum 2 years from today. How much more will you have to deposit as a lump sum if you wait for 2 years before making the deposit? A)$1414.14 B)$2319.47 C)$2891.11 D)$3280.78 E)$3406.78 Question 2 Samantha opened a savings account this morning
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TIME VALUE Time Value • Interest Rates • Compounding • Discounting • Effective Rates • Annuities • Perpetuities 2 Interest Rates • Types – Bank rate vs. Prime rate – Mortgage rates – Deposit‚ Loan‚ Credit rates • Movement – Demand / Supply – Inflation/ Deflation – Government intervention 3 Main Components 1. Real 2. Inflation 3. Risk *Note: - Risk Free (Rf) = Real + Inflation - Nominal = Rf + Risk Premium 4 Risk Free & Real Rate • Risk Free (Rf) = Real +
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FVA. 8. Here we have the FVA‚ the length of the annuity‚ and the interest rate. We want to calculate the annuity payment. Using the FVA equation: FVA = C{[(1 + r)t – 1] / r} $40‚000 = $C[(1.05257 – 1) / .0525] We can now solve this equation for the annuity payment. Doing so‚ we get: C = $40‚000 / 8.204106 C = $4‚875.55 9. Here we have the PVA‚ the length of the annuity‚ and the interest rate. We want to calculate the annuity payment. Using the PVA equation: PVA = C({1 –
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Chapter 6 The Time Value of Money-Annuities and Other Topics 6.1 Annuities 1) You wish to borrow $2‚000 to be repaid in 12 monthly installments of $189.12. The annual interest rate is: A) 24%. B) 8%. C) 18%. D) 12%. 2) If you have $20‚000 in an account earning 8% annually‚ what constant amount could you withdraw each year and have nothing remaining at the end of five years? A) $3‚525.62 B) $5‚008.76 C) $3‚408.88 D) $2‚465. 3) If you invest $750 every six months at 8% compounded semi-annually
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part of the loan package Formulas: Uneven Cashflow Even Cashflow * Annuity – series of equal payments (“PMT”) that occur at regular intervals for a period of time (“t”). * Payment is normally made at the end of the period. For payment occurs at the beginning of the period‚ it is Annuity Due. Perpetuity – infinite series of equal payments Formula: Annuities Formula: Perpetuities When n → ∞‚ PV (Perpetuity) =
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Slide 4.1 Corporate Financial Management‚ 5th edition Glen Arnold Mathematical Tools For Time Value of Money Glen Arnold‚ Corporate Financial Management‚ 5th Edition © Pearson Education Limited 2013 Slide 4.2 Simple Interest and Future Value • Simple interest A sum of £10 is deposited in a bank account that pays 12 per cent per annum. At the end of year 1 the investor has £11.20 in the account. F = P(1 + i) 11.20 = 10(1 + 0.12) where F = Future value‚ P = Present value‚ i
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though it involves more calculation. An annuity is a stream of constant cash flows (payments and receipts) occurring at regular intervals of time. The premium payments of a life insurance policy‚ for example are an annuity.When the cash flows occur at the end of each period‚ the annuity is called an ordinary annuity or a deferred annuity.When the cash flows occur at the beginning of each period‚ the annuity is called an annuity due. The future value of an annuity- FVAn=A(1+r)n-1+A(1+r)n-2+…..+A
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207)= $593‚295 Duration= 20 years Annual rate of return= 10% Annuity Ordinary=?? Using Table A-3 Annuity ordinary= 593‚295/57.274= 10‚358.88 to be paid at every year end 2. Deposits to create a perpetuity You have decided to endow your favorite university with a scholarship. It is expected to cost $ 6‚000 per year to attend the university into perpetuity. You expect to give the university the endowment in 10 years and will accumulate
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Sum. (PVIFi‚n) -n Future Value of an Annuity. (FVIFAi‚n) FVAn = CF 4 Present Value of an Annuity. (PVIFAi‚n) 1 - ( 1 + i )-n PVAn = CF i 5 Present Value of Perpetuity. (PVA ) 6 Effective Annual Rate given the APR. 7 The length of time required for a PV to grow to a FV. 8 The APR required for a PV to grow to a FV. 9 Present Value of a Growing Annuity. 10 Present Value of a Growing Perpetuity. 11 The length of time required for
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