Question

1. Solve for the unknown interest rate in each of the following: (Do not round intermediate calculations and round your final answers to 2 decimal places.)

   

Present Value				Years		Interest Rate		Future Value
	$	240		4		%		$	297
		360		18		%			1,080
		39,000		19		%			185,382
		38,261		25		%			531,618

2. At 6.5 percent interest, how long does it take to double your money? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  

Length of time

years

  

At 6.5 percent interest, how long does it take to quadruple it? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  

Length of time

years

3. Normandin Inc. has an unfunded pension liability of $575 million that must be paid in 20 years. To assess the value of the firm’s stock, financial analysts want to discount this liability back to the present.

  

If the relevant discount rate is 6.8 percent, what is the present value of this liability? (Enter your answer in dollars, not millions of dollars. Do not round intermediate calculations and round your final answer to 2 decimal places.)

   

Present value

$

4. Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2003, Sothebys sold the Edgar Degas bronze sculpture Petit Danseuse de Quartorze Ans at auction for a price of $10,311,500. Unfortunately for the previous owner, he had purchased it in 1999 at a price of $12,377,500.

  

What was his annual rate of return on this sculpture? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your final answer to 2 decimal places.)

   

Annual rate of return

%

5. Suppose you are committed to owning a $190,000 BMW. If you believe your mutual fund can achieve a 12 percent annual rate of return and you want to buy the car in nine years on the day you turn 30, how much must you invest today? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

  

Investment

$

6. You are scheduled to receive $15,000 in two years. When you receive it, you will invest it for six more years at 7.1 percent per year. How much will you have in eight years? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

  

Future value

$

Answer 1

1.

Present Value	Years	Interest Rate	Future Value
$240	4	5.47%	$297
360	18	6.29%	1,080
39,000	19	8.55%	185,382
38,261	25	11.10%	531,618

Explanation:

PV and FV are related as:

PV = FV/ (1+r) n

r = Rate of interest

n = Number of periods

i)

$ 240 = $ 297 /(1+r)4

(1+r)4 = $ 297/$ 240 = 1.2375

1+r = (1.2375)1/4 = (1.2375)0.25 =1.05471786420082

r = 1.05471786420082 -1 = 0.05471786420082 or 5.57 %

ii)

$ 360 = $ 1,080 /(1+r)18

(1+r)18 = $ 1,080/$ 360 = 3

1+r = (3)1/18 = (3) 0.055555556 = 1.06293507041105

r = 1.06293507041105 -1 = 0.06293507041105 or 6.29 %

iii)

$ 39,000 = $ 185,382 /(1+r)19

(1+r)19 = $ 185,382/$ 39,000 = 4.75338461538462

1+r = (4.75338461538462)1/19 = (4.75338461538462) 0.0526315789473684

= 1.08550476584235

r = 1.08550476584235 – 1 = 0.08550476584235 or 8.55 %

iv)

$ 38,261 = $ 531,618 /(1+r)25

(1+r)25 = $ 531,618/$ 38,261 = 3

1+r = (13.894513995975)1/25 = (13.894513995975) 0.04 = 1.11099916982758

r = 1.11099916982758 -1 = 0.11099916982758 or 11.10 %

2.

As per rule 72, time required to double the investment is:

T = 72/Rate of interest

= 72/6.5 = 11.07692308 or 11.08 years

As per rule 144, time required to quadruple the investment is:

T = 144/ Rate of interest

= 144/6.5

= 22.1538461538 or 22.15 years

3.

PV = FV/ (1+r) n

    = $ 575,000,000/ (1+0.068)20

    = $ 575,000,000/ (1.068)20

    = $ 575,000,000/ 3.72756352870894

     = $ 154,256,257.625515 or $ 154,256,257.63

4.

Total Return Rate = (Final price – Initial price)/Initial price

                        = ($ 10,311,500 - $ 12,377,500)/ $ 12,377,500

                       = - $ 2,066,000/$ 12,377,500

                      = - 0.166915774590992

Annual rate of return = (1+ Total Return Rate)1/years - 1

                                      = (1- 0.166915774590992)1/4 – 1

                                     = (0.833084225409008)0.25 - 1

                                       = 0.955371381687618 – 1

                                       = -0.044628618312382 or - 4.46 %