Calculate the present value of the following annuity streams:

a. $5,000 received each year for 6 years on the last day of each year if your investments pay 7 percent compounded annually.

b. $5,000 received each quarter for 6 years on the last day of each quarter if your investments pay 7 percent compounded quarterly.

c. $5,000 received each year for 6 years on the first day of each year if your investments pay 7 percent compounded annually.

d. $5,000 received each quarter for 6 years on the first day of each quarter if your investments pay 7 percent compounded quarterly.

Answer a.

Annual Payment = $5,000
Time Period = 6 years
Annual Interest Rate = 7.00%

Present Value = $5,000/1.07 + $5,000/1.07^2 + … + $5,000/1.07^5 + $5,000/1.07^6
Present Value = $5,000 * (1 - (1/1.07)^6) / 0.07
Present Value = $5,000 * 4.766540
Present Value = $23,832.70

Answer b.

Quarterly Payment = $5,000
Time Period = 6 years or 24 quarters

Annual Interest Rate = 7.00%
Quarterly Interest Rate = 7.00% / 4
Quarterly Interest Rate = 1.75%

Present Value = $5,000/1.0175 + $5,000/1.0175^2 + … + $5,000/1.0175^23 + $5,000/1.0175^24
Present Value = $5,000 * (1 - (1/1.0175)^24) / 0.0175
Present Value = $5,000 * 19.460686
Present Value = $97,303.43

Answer c.

Annual Payment = $5,000
Time Period = 6 years
Annual Interest Rate = 7.00%

Present Value = $5,000 + $5,000/1.07 + $5,000/1.07^2 + … + $5,000/1.07^4 + $5,000/1.07^5
Present Value = $5,000 * 1.07 * (1 - (1/1.07)^6) / 0.07
Present Value = $5,000 * 5.100197
Present Value = $25,500.99

Answer d.

Quarterly Payment = $5,000
Time Period = 6 years or 24 quarters

Annual Interest Rate = 7.00%
Quarterly Interest Rate = 7.00% / 4
Quarterly Interest Rate = 1.75%

Present Value = $5,000 + $5,000/1.0175 + $5,000/1.0175^2 + … + $5,000/1.0175^22 + $5,000/1.0175^23
Present Value = $5,000 * 1.0175 * (1 - (1/1.0175)^24) / 0.0175
Present Value = $5,000 * 19.801248
Present Value = $99,006.24