Question

Calculate the future value of the following annuity streams:

a. $6,000 received each year for 4 years on the last day of each year if your investments pay 6 percent compounded annually.
b. $6,000 received each quarter for 4 years on the last day of each quarter if your investments pay 6 percent compounded quarterly.
c. $6,000 received each year for 4 years on the first day of each year if your investments pay 6 percent compounded annually.
d. $6,000 received each quarter for 4 years on the first day of each quarter if your investments pay 6 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

a.Future Value = P*[{(1+r)ⁿ-1}/r]

= 6,000[{(1+0.06)⁴-1}/0.06]

= $26,247.70

b.Number of periods = 4*4 = 16

Rate per Quarter = 6/4 = 1.5%

Future Value = 6,000[{(1+0.015)¹⁶-1}/0.015]

= $107,594.22

c.Future Value of Annuity Due = (1+r)* P*[{(1+r)ⁿ-1}/r]

= (1+0.06)* 6,000[{(1+0.06)⁴-1}/0.06]

= $27,822.56

d. Future Value = (1+0.015)*6,000[{(1+0.015)¹⁶-1}/0.015]

= $109,208.13