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The present value of a perpetuity is A/r, where A is the periodic payment to be received forever.

may be handled in a similar fashion as single payments if we use annuity factors instead of single-payment factors. The present value, PV, is the future value, FV, times the present value factor, (1 + r) − N . <span>The present value of a perpetuity is A/r, where A is the periodic payment to be received forever. It is possible to calculate an unknown variable, given the other relevant variables in time value of money problems. The cash flow additivity principle c

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When you make a single investment today, its future value, received N years from now, is as follows: FV = future value at time n PV = present value r = interest rate per period N = number of years A key assumption of the future valu

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make a single investment today, its future value, received N years from now, is as follows: FV = future value at time n PV = present value r = interest rate per period N = number of years <span>A key assumption of the future value formula is that interim interest earned is reinvested at the given interest rate (r). This is known as compounding. In order to receive a single future cash flow N years from now, you must make an investment today in the following amount:

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e n PV = present value r = interest rate per period N = number of years A key assumption of the future value formula is that interim interest earned is reinvested at the given interest rate (r). This is known as compounding. <span>In order to receive a single future cash flow N years from now, you must make an investment today in the following amount: Notice that the future cash flow is discounted back to the present. Therefore, the interest rate is called the discount rate. You sh

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ulator keys to press are: If you are given the FV and need to solve for PV, the calculator keys to press are: When compounding periods are not annual <span>Some investments pay interest more than once a year. When you calculate these amounts, make sure that periodic interest rates correspond to the number of compounding periods in the year. For example, if time periods are quoted in quarters, quarterly interest rates should be used. When compounding periods are other than annual 

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. When you calculate these amounts, make sure that periodic interest rates correspond to the number of compounding periods in the year. For example, if time periods are quoted in quarters, quarterly interest rates should be used. <span>When compounding periods are other than annual r s = the quoted annual interest rate m = the number of compounding periods per year N = the number of years. Example 2 An analyst invests $5 million in a 5-year certificate of deposit (CD) at a local financial institution. The CD promises to pay 7% per year, compounded semi-a

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. When you calculate these amounts, make sure that periodic interest rates correspond to the number of compounding periods in the year. For example, if time periods are quoted in quarters, quarterly interest rates should be used. <span>When compounding periods are other than annual r s = the quoted annual interest rate m = the number of compounding periods per year N = the number of years. Example 2 An analyst invests $5 million in a 5-year certificate of deposit (CD) at a local financial institution. The CD promises to pay 7% per year, compounded semi-a

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t? The calculator keys to press are: Note that the answer is greater than when the compounding was annual. This is because interest is earned twice a year instead of only once. <span>If the number of compounding periods becomes infinite, interest is compounding continuously. Accordingly, the future value N years from now is computed as follows: <span><body><html>

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Annuity is a finite set of sequential cash flows, all with the same value. Ordinary annuity has a first cash flow that occurs one period from now (indexed at t = 1). In other words, the payments occur at the end of each period. Future value

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ity is a finite set of sequential cash flows, all with the same value. Ordinary annuity has a first cash flow that occurs one period from now (indexed at t = 1). In other words, the payments occur at the end of each period. <span>Future value of a regular annuity where A = annuity amount N = number of regular annuity payments r = interest rate per period Present valu

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he end of each period. Future value of a regular annuity where A = annuity amount N = number of regular annuity payments r = interest rate per period <span>Present value of a regular annuity Annuity due has a first cash flow that is paid immediately (indexed at t = 0). In other words, the payments occur at the beginning of

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sent value of a regular annuity Annuity due has a first cash flow that is paid immediately (indexed at t = 0). In other words, the payments occur at the beginning of each period. <span>Future value of an annuity due This consists of two parts: the future value of one annuity payment now, and the future value of a regular annuity of (N -1) period. Calculate the two parts and add them together. Alternatively, you can use this formula: Note that, all other factors being equal, the future value of an annuity due is equal to the future value of an ordinary annuity multiplied by

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sent value of a regular annuity Annuity due has a first cash flow that is paid immediately (indexed at t = 0). In other words, the payments occur at the beginning of each period. <span>Future value of an annuity due This consists of two parts: the future value of one annuity payment now, and the future value of a regular annuity of (N -1) period. Calculate the two parts and add them together. Alternatively, you can use this formula: Note that, all other factors being equal, the future value of an annuity due is equal to the future value of an ordinary annuity multiplied by

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future value of one annuity payment now, and the future value of a regular annuity of (N -1) period. Calculate the two parts and add them together. Alternatively, you can use this formula: Note that, <span>all other factors being equal, the future value of an annuity due is equal to the future value of an ordinary annuity multiplied by (1 + r). Present value of an annuity due This consists of two parts: an annuity payment now and the present value of a regular annuity of (N - 1) period. Use the a

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u can use this formula: Note that, all other factors being equal, the future value of an annuity due is equal to the future value of an ordinary annuity multiplied by (1 + r). <span>Present value of an annuity due This consists of two parts: an annuity payment now and the present value of a regular annuity of (N - 1) period. Use the above formula to calculate the second part and add the two parts together. This process can also be simplified to a formula: Note that, all other factors being equal, the present value of an annuity due is equal to the present value of an ordinary annuity multiplied

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e present value of a regular annuity of (N - 1) period. Use the above formula to calculate the second part and add the two parts together. This process can also be simplified to a formula: Note that, <span>all other factors being equal, the present value of an annuity due is equal to the present value of an ordinary annuity multiplied by (1 + r). Hint: Remember these formulas - you can use them to solve annuity-related questions directly, or to double-check the answers given by your calculator. A perpe