Question

Calculate the future value of the following annuity streams:

a. $4,000 received each year for 4 years on the last day of each year if your investments pay 5 percent compounded annually.
b. $4,000 received each quarter for 4 years on the last day of each quarter if your investments pay 5 percent compounded quarterly.
c. $4,000 received each year for 4 years on the first day of each year if your investments pay 5 percent compounded annually.
d. $4,000 received each quarter for 4 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))

Answer 1

A-	Future value of investment	Annuity amount*FVAF at 5% for 4 Years	4000*4.31012	10.03574398
	Annuity amount			4000
	FVAF at 5% for 4 years =(1+r)^n-1/ r	(1.05)^4 -1 / 5%	.215506/5%	4.31012
B-	Future value of investment at the end of 16th quarter	Annuity amount*FVAF at 1.25% for 16 quarters	4000*17.59116	70364.64
	Annuity amount per quarter			4000
	FVAF at 1.25% for 16 quarters =(1+r)^n-1/ r      r =5/4 =1.25%   n =4*4 =16	(1.0125)^16 -1 / 1.25%	.219889/5%	17.59116
C-	Future value of investment in case of annuity due	Annuity amount*FVAF at 5% for 4 Years in case of annuity due	4000*4.525626	18102.504
	Annuity amount			4000
	FVAF at 5% for 4 years =(1+r)^n-1/ r	(1.05)^4 -1 / 5%	.215506/5%	4.31012
	FVAF at 5% for 4 years in case of annuity due	FVAF at 5% for 4 Years*(1+r)	4.31012*(1.05)	4.525626
D-	Future value of investment at the end of 16th quarter inn case of annuity due	Annuity amount*FVAF at 1.25% for 16 quarters in case of annuity due	4000*17.81104	71244.16
	Annuity amount per quarter			4000
	FVAF at 1.25% for 16 quarters =(1+r)^n-1/ r      r =5/4 =1.25%   n =4*4 =16	(1.0125)^16 -1 / 1.25%	.219889/5%	17.59116
	FVAF at 1.25% for 16 quarters in case of annuity due =(1+r)^n-1/ r      r =5/4 =1.25%   n =4*4 =16	FVAF at 1.25% for 16 quarters*(1+r)	17.59116*(1.0125)	17.8110495