Question

1)How much money do you need to deposit into an account annually if you desire to have $9 million in 45 years. Assume a 4% annual interest rate, compounded annually. Your first deposit will occur at the end of the first year.

2) Your machine operator is becoming more productive and generates additional profit each year. You expect to receive $39,000 in profit at the end of the year, but this will increase by 8% a year for the next 10 years. If you have a 11% annual interest rate on your investments (compounded annually), what is the Present Value of the profits over the next 10 years?

3) What is the Present Value of a $16,000 inflow 4 years from now, a $45,000 inflow 11 years from now, and a $35,000 outflow 6 years from now. Assume an interest rate of 4% for years 1-4, 6% for years 5-6, and 8% for years 7-11. Assume annual compounding. Your answer could be negative.

4) A woman wins the lottery worth $8.74 million. The woman receives an immediate check for $641,000, and she plans to receive 24 annual checks of $337,458, with the first check coming exactly one year from now. If a buyer offers to purchase the 24 remaining checks for $6.72 million to be paid immediately, what is the buyer's annual interest rate? State your answer as a percentage with decimals. In other words, enter 8.3 not 0.083.

Answer 1

(1)

Required amount = $9,000,000 / F/A(4%, 45) = $9,000,000 / 121.0294** = $74,362.10

**From F/A Factor table

(2)

Present value (PV) is computed as follows. Note that

• Profit in year N = Profit in year (N - 1) x 1.08 [i.e. Profit in year 1 = $39,000 x 1.08 = $42,120]
• PV factor in year N = (1.11)^-N.

Year	Profit ($)	PV factor @11%	Discounted PV ($)
	(A)	(B)	(A) x (B)
1	42,120	0.900900901	37,946
2	45,490	0.811622433	36,920
3	49,129	0.731191381	35,923
4	53,059	0.658730974	34,952
5	57,304	0.593451328	34,007
6	61,888	0.534640836	33,088
7	66,839	0.481658411	32,194
8	72,186	0.433926496	31,324
9	77,961	0.390924771	30,477
10	84,198	0.352184479	29,653
		Present Value ($) =	3,36,483

NOTE: As HOMEWORKLIB Answering Policy, 1st 2 questions have been answered.