Question

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Calculate the future value of the following annuity streams: a. $4,00O received each year for 6 years on the last day of each year if your investments pay 5 percent compounded annually b. $4,00O received each quarter for 6 years on the last day of each quarter if your investments pay 5 percent compounded quarterly c. $4,0OO received each year for 6 years on the first day of each year if your investments pay 5 percent compounded annually d. $4,000 received each quarter for 6 years on the first day of each quarter if your investments pay 5 percent compounded quarterly. (For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g.. 32.16)) a. Future value b. Future value C. Future value d. Future value

Answer 1

Answer (a), (b), (c) and (d):

Workings:

Answer a:

Annuity received at the end of each year = $4000

Time period = 6 years

Interest rate = 5% compounded annually

To calculate future value (FV) we will use FV function of excel:

= FV (rate, nper, pmt, pv, type)

= FV (5%, 6, -4000, 0, 0)

= $27,207.65

Future value = $27,207.65

Answer (b):

Amount received on last day of each quarter = $4000

Time period = 6 years = 6 * 4 = 24 quarters

Interest rate = 5% compounded quarterly

Quarterly interest = 5%/4 = 1.25%

= FV (1.25%, 24, -4000, 0, 0)

= $111,152.34

Future value = $111,152.34

Answer (c):

Annuity received on first day of each year = $4000

Time period = 6 years

Interest rate = 5% compounded annually

= FV (5%, 6, -4000, 0, 1)

= $28,568.03

Future value = $28,568.03

Answer (d):

Amount received on the first day of each quarter = $4000

Time period = 6 years = 6 * 4 = 24 quarters

Interest rate = 5% compounded quarterly

Quarterly interest = 5%/4 = 1.25%

= FV (1.25%, 24, -4000, 0, 1)

= $112,541.74

Future value = $112541.74