Consider an n-year increasing annuity payable annually in arrears, where the rate of payment at the end of the first year is £1, the payment at the end of the second year is £2, and so on until the final payment at the end of year n is of amount En. Show that the present value of this annuity is given by: ἅπι – ηνη (la)n\ = i
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- Calculate the future value of the following annuities, assuming each annuity payment is made at the end of each compounding period. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use appropriate factor(s) from the tables provided. Round your answers to 2 decimal places.) 1. 2. 3. Annuity Annual Payment Rate $4,700 6.0 % 8.0 % 7,700 6,700 10.0 % Show Transcribed Text 1. 2. 3. Annuity Annual Payment Rate Interest Compounded Quarterly Annually Semiannually $ 5,700 Interest Compounded 8.0 % Quarterly 10,700 11.0% Annually 4,700 10.0 % Semiannually Period Invested 5 years 6 years 9 years Calculate the present value of the following annuities, assuming each annuity payment is made at the end of each compounding period. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use appropriate factor(s) from the tables provided. Round your answers to 2 decimal places.) $ Period Invested 2 years 5 years 3 years Future Value of Annuity 172,892.28 Present Value of AnnuityCalculate the future value of the following annuities, assuming each annuity payment is made at the end of each compounding period. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use appropriate factor(s) from the tables provided. Round your answers to 2 decimal places.) Annuity Payment Annual Rate Interest Compounded Period Invested Future Value of Annuity 1. $3,100 8.0 % Semiannually 9 years $79,500.77 2. 6,100 10.0 % Quarterly 5 years 3. 5,100 12.0 % Annually 6 yearsFor each of the following situations involving annuities, solve for the unknown. Assume that interest is compounded annually and that all annuity amounts are received at the end of each period. (i = interest rate, and n = number of years) (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) Present Value Annuity Amount i = n = $3,000 75,000 20,000 80,518 1 2 3 4 5 242,980 161,214 500,000 250,000 8% 9% 10% 5 4 8 4
- Calculate the present value of the following annulties, assuming each annuity payment is made at the end of each compounding period. (FV of $1, PV of $1, FVA of $1, and PVA of S1) (Use tables, Excel, or a financial calculator. Round your answers to 2 decimal places.) \table[[, \table[[Annuity], [Payment]], \table [[ Annual], [Rate]], \table[[Interest], [Compounded]], \table [[Period], [Invested]], \table [[Present Value of], [ Annuity]]], [1., $5,000, 7.0%, Semiannually,3 years,], [2., 10, 000, 8.0%, Quarterly,2 years, ], [3., 4,000, 10.0 %, Annually,5 years,]]The present value of an ordinary annuity, PAN, is the value today that would be equivalent to the annuity payments (PMT) received at fixed intervals over the annuity period. The equation is: Each payment of an annuity due is discounted for one less (1 + I). The equation is: PVAN= PMT 1- (1+1)N I period, so the present value of an annuity due is equal to the present value of an ordinary annuity multiplied by PVA due PVA ordinary (1+1) One can solve for payments (PMT), periods (N), and interest rates (I) for annuities. The easiest way to solve for these variables is with a financial calculator or a spreadsheet. Quantitative Problem 1: You plan to deposit $1,700 per year for 5 years into a money market account with an annual return of 2%. You plan to make your first deposit one year from today. a. What amount will be in your account at the end of 5 years? Do not round intermediate calculations. Round your answer to the nearest cent. $ b. Assume that your deposits will begin today. What…For each of the following situations involving annuities, solve for the unknown. Assume that interest is compounded annually and that all annuity amounts are received at the end of each period. (i=interest rate, and n=number of years)(FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of 1$ and PVAD of $1) (Use appropriate factor (s) from the tables provided. Round your final answers to nearest whole dollar amount.) Present Value Annuity Amount i= n= ______________ $ 2,600 8% 5 507,866 135,000 _____ 4 661,241 170,000 9% ____ 540,000 78,557 _____ 8 230,000 _____________ 10% 4
- For each of the following situations involving annuities, solve for the unknown. Assume that interest is compounded annually and that all annuity amounts are received at the end of each period. (i = interest rate, and n = number of years) (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided. Round your final answers to nearest whole dollar amount.) Present Value Annuity Amount i = n = 1. ? $2,400 8% 5 2. 533,082 140,000 ? 4 3. 583,150 180,000 9% ? 4. 530,000 75,502 ? 8 5. 235,000 ? 10% 4Annuity A pays 1 at the beginning of each year for five years.Annuity B pays 1 at the beginning of each year for four years.The Macaulay duration of Annuity A at the time of purchase is Σ/10. Both annuities offer thesame yield rate.Calculate the Macaulay duration of Annuity B at the time of purchase. Σ=22To find the present value (PV) of an ordinary annuity, a. the interest is compounded and then subtracted from the FV. O b. each payment is divided by (1+1)* c. each payment is multiplied by (1+1). O d. the future value (FV) is divided by the interest rate. e. the future value is divided by (1+1)*:
- For each of the following situations involving annuities, solve for the unknown. Assume that interest is compounded annually and that all annuity amounts are received at the end of each period. (i = interest rate, and n = number of years) (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided. Round your final answers to nearest whole dollar amount.)The ___________ of an annuity is the amount that must be invested now at interest rate i per time period to provide n payments each of amount R.To determine the converted table factor for the present value of an annuity due, one must find the factor for the present value of an ordinary annuity for n + 1 and then add 1. n − 1 and then subtract 1. n − 1 and then add 1. n + 1 and then subtract 1.