An annuity is payable continuously for n years. The rate of payment is constant through each year and is as follows: 1 unit per annum during the first year; 2 units per annum during the second year; 3 units per annum during the third year; and so on until the final year n. Show that the present value of the annuity is given by: ἅπι (la) n = -ηνη δ Hint: You have to show your full workings from basic principles of valuing a constant payment stream.

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…

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.

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% 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= ______________          $                 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.)

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.)         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 years

Find the value of the annuity at the end of the indicated number of years. Assume that the interest is compounded with the same frequency as the deposit. M=$200 N=semiannually R=8% T=25

The following terms of payment for an annuity are as follows:Periodic payment = P20,000Payment interval = 1 monthInterest rate = 18% compounded monthly Terms = 15 years1. Find the present worth paid of all the payments if it is paid at the end of each month. 2. Find the difference between the sums of an annuity due and an ordinary annuity on these payments. 3. Find the difference between the present values of an annuity due and an ordinary annuity based on these payments. Anwers. 1. P1,214,911.246 2. P271,687.35 3. P18,628.67

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. (/= interest rate, and n= number of years) Note: Use tables, Excel, or a financial calculator. Round your final answers to nearest whole dollar amount. (FV of $1. PV of $1. FVA of $1. PVA of $1. EVAD of $1 and PVAD of $1) 1. $ 2 3 4. 15 Present Value Answer is complete but not entirely correct. Annuity Amount 2.200 145,000 190,000 72.523 45,787 8,784 558,865 480,945 520,000 240,000 8% 1.0% 9% 2.5% 10% n= 5 4 30 8 4