# Present Value of Annuity Streams

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How would you calculate the present and future value of the following annuity streams?

a. $5,000 received each year for 5 years on the last day of each year if your investments pay 6 percent compounded annually.

b. $5,000 received each quarter for 5 years on the last day of each quarter if your investments pay 6 percent compounded quarterly.

c. $5,000 received each year for 5 years on the first day of each year if your investments pay 6 percent compounded annually.

d. $5,000 received each quarter for 5 years on the first day of each quarter if your investments pay 6 percent compounded quarterly.

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##### Solution Summary

This solution calculates both the present and future values for the identified annuity streams. Excel is used for future value calculations. Inputs for present value calculations are identified and can be easily plugged in to a financial calculator. Adjustments for PV of an annuity in advance from an annuity in arrears are calculated as well.

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a. $5,000 received each year for 5 years on the last day of each year if your investments pay 6 percent compounded annually.

Cash Flow Stream: Annuity

Type of annuity: Arrears

Annual cash flow C= $5,000

Number of years t = 5 years

Frequency of compounding in a year f= 1

Annual Interest rate R= 6%

Interest rate for compouding period r = R/f=6%/1=6%

PV of an annuity in arrears=C/r*(1-1/(1+r)^(f*t))= 5000/6%*(1-1/(1+6%)^(1*5))=$21061.82

b. $5,000 received each quarter for 5 years on the last day of each quarter if your investments pay 6 percent compounded quarterly.

Cash Flow Stream: ...

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