Question

Example 1: Future Value (FV) of a Present Single Sum

Your client has $500,000 in an IRA and has asked you to estimate

its value when the client reaches retirement age in 8 years, assuming

a 6% return each year.

Example 2: Future Value (FV) of a present single Sum with

Multiple Interest Rates

Same facts as Example 1 except the client would like to adjust the

asset allocation of the investments over time, evolving from a

more aggressive strategy during the earlier years intro a more

conservative investment approach as she approaches retirement.

Thus, she projects to earn a 10% annnual return during the first

two years of the investment period, and 8%, 6%, and 4% returns

over each of the next two-year periods, respectively.

Example 3: Future Value (FV) of a Series of Payments (Annuity Due)

Your client would like to contribute $12,000 to a retirement account

at the beginning of each year for the next 20 years, earning an

annual return of 6%.

Example 4: Future Value (FV) of a Series of Payments (Ordinary Annuity)

Your client to make monthly deposits to the retirement account. Assume

your client makes deposits of $1,000 at the end of each month for

20 years and earns 6% per year on his investments over that time.

Example 5: Future Value (FV) of a Series of Payments (Ordinary Annuity)
	to Combine with Existing Retirement Account
Using the same facts as Example 4 but further assume that the client
already has accumulated $200,000 in retirement savings.

Answer 1

1)
Future Value	= Amount(1+i)^N
	=500000(1+0.06)^8
	=796924.04
2)
Future Value	= Amount(1+i)^N
	=500000(1.1*1.1*1.08*1.08*1.06*1.06*1.04*1.04)
	=857593.13
3)
Future Value of Annuity Due	={Amount[(1+i)^N-1](1+i)}/i
	={12000[(1.06)^20-1](1.06)}/0.06
	=467912.72
4)
Future Value of Ordinary Annuity	=Amount[(1+i)^N-1]/i
	=1000[(1.06)^20-1]/0.06
	=36785.59
5)
Future Value of accumulated sum	= Amount(1+i)^N
	=200000(1+0.06)^20
	=641427.09
Future Value of Ordinary Annuity	=Amount[(1+i)^N-1]/i
	=1000[(1.06)^20-1]/0.06
	=36785.59
Future Value of total value invested	=641427.09+36785.59
	=678212.68