Question

6. Calculate the value of the cash flows at time 6. The interest rate is 9.9%.

0	1	2
$1,120	$2,163	$3,290

7. In 1998, the average price of a gallon of gas was $1.01. Today, the average price of a gallon of gas is $2.87. At what annual rate has a gallon of gas increased over the last 20 years? (Answer as a percent. Enter only numbers and decimals in your response. Round to 2 decimal places.)

8. You are buying an investment property for $393,580 today. Through research, you have determined that the value of the property is likely to grow at a rate of 7.16% per year, on average. How long until the value of the property grows to $546,287?

9. Your goal is to have $76,386. If you can earn 10.78% per year and you invest $19,812 today, how many years until you reach your goal?

10. You are looking at an investment that will pay you $22,339 in year 2, $43,709 in year 4 and $45,031 in year 6. If your required return is 8.16%, what is the most you should pay for the investment? (In other words, how much is the project worth today?)

Answer 1

Solution 6
	Year	Cashflow	FV factor, (1+9.90%)^(6-t)	Cashflow*FV factor
	0	$ 1,120.00	1.761919875	$ 1,973.35
	1	$ 2,163.00	1.603202798	$ 3,467.73
	2	$ 3,290.00	1.458783256	$ 4,799.40
			Total	$10,240.47
Solution 7
	1998 price	1.01
	Price after 20 years	2.87
	Time period	20
	Price after 20 years=	Price in 1998*(1+r)^time
	2.87=	1.1*(1+r)^20
	2.87/1.1=	(1+r)^20
	2.609090909	=(1+r)^20
	(1+r)=	(2.60909090909091)^(1/20)
	(1+r)=	1.0491183
	R=	0.0491183
	R=	4.91%
Solution 8
	Investment	$   393,580
	Amount	$   546,287
	Period in years	T
	Interest	7.16%
	Amount=	Investment* (1+Interest)^Time
	546287=	393580*(1+7.16%)^T
	546287/393580=	(1.0716)^T
	1.387994817	(1.0716)^T
	Log 1.3879948168098=	T Log 1.0716
	0.142387844335619=	T*0.0300327049361713
	T=	0.142387844335619/0.0300327049361713
	T=	4.74	Years
Solution 9
	Investment	$     19,812
	Amount	$     76,386
	Period in years	T
	Interest	10.78%
	Amount=	Investment* (1+Interest)^Time
	76386=	19812*(1+10.78%)^T
	76386/19812=	(1.1078)^T
	3.85554209569958=	(1.0716)^T
	Log 3.85554209569958=	T Log 1.1078
	0.586085449	T*0.0444613608106648
	T=	0.586085449214303/0.0444613608106648
	T=	13.18	Years
Solution 10
	Year	Cashflow	PV factor, 1/(1+8.16%)^(t)	Cashflow*PV factor
	2	$22,339.00	0.854804191	$19,095.47
	4	$43,709.00	0.730690205	$31,937.74
	6	$45,031.00	0.62459705	$28,126.23
			Present worth	$79,159.44