# Present Value of Annuity Streams

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 This solution is **FREE** courtesy of BrainMass!

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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: Annuity

Type of annuity: Arrears

Quarterly cash flow C= $5,000

Number of years t = 5 years

Frequency of compounding in a year f= 4

Annual Interest rate R= 6%

Interest rate for compouding period r = R/f=6%/4=1.5%

PV of an annuity in arrears=C/r*(1-1/(1+r)^(f*t))= 5000/1.5%*(1-1/(1+1.5%)^(4*5))=$85843.19

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

Cash Flow Stream: Annuity

Type of annuity: Advance

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 advance =PVof annuity in arrears * (1+r) = $21061.82*(1+6%)=$22325.53

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

Cash Flow Stream: Annuity

Type of annuity: Advance

Quarterly cash flow C= $5,000

Number of years t = 5 years

Frequency of compounding in a year f= 4

Annual Interest rate R= 6%

Interest rate for compouding period r = R/f=6%/4=1.5%

PV of an annuity in advance =PVof annuity in arrears * (1+r) = $85843.19*(1+1.5%)=$87130.84

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FUTURE VALUE

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Check the attached sheet. The calculation are complex to do manual thats why excel is used.

You can also use Future Value of Annuity tables to computes Future value

Future Value Annuity Factor for 5 payments for 6% = 5.637

So,

(a) Future Value = 5000*5.637 = $28,185

Future Value Annuity Factor for 20 (5*4) quarterly payments for 1.5% per quarter = 23.124

(b) Future Value = 5000*23.124 = $115,620

Similiary for (c) Future Value = 5000*5.975 = $29,875

(d) Future value = 5000*23.471 = $117,355

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