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UE OF MONEY HOMEWORK WORKSHEET eferences Mailings Review View Help Tell me wihat

ID: 2400687 • Letter: U

Question

UE OF MONEY HOMEWORK WORKSHEET eferences Mailings Review View Help Tell me wihat you want to do "?.lan..: . |__, A .AE | AaBbCcDi AaBbC AaBbCcl|AaBbCcD(1 AaBbc a-? Heading 1. Heading 2 1 Normal Strong Paragraph Styles 12. You borrow $50,000 an d will make monthly payments for 2 years at 12% interest. How much will those payments be 13. You just won a contest that will pay you $15,000 each year, for five years. Assuming a 12% discount rate, what is the present value of your contest winnings? 14. John plans to retire in 12 years. When he retires, he would like to take an extended vacation, which he expects will cost at least $40,000. What lump-sum amount must he invest now to have the needed $40,000 at the end of 12 years if he invests at A) 8%? B) 12%? 15. If John chooses to invest money each year to fund his vacation in 12 years, how much money must he invest at the end of each year to have $40,000 to fund his vacation if he invests at A) 8%? B) 12%?

Explanation / Answer

12.

Monthly payments can be computed using Present value of annuity concept as:

PV = C x PVIFA(r, n)

r = rate of interest = 12 % p.a. or 1% p.m.

n = No. of periods = 12 months x 2 years = 24 periods

$ 50,000 = C x PVIFA (1 %, 24)

$ 50,000 = C x 21.243

C = $ 50,000/21.243

   = $ 2,353.72

13.

PV = C x PVIFA(r, n)

r = rate of interest = 12 % p.a.

n = No. of periods = 5

C = Cash flow per period = $ 15,000

PV = $ 15,000 x PVIFA (12 %, 5)

     = $ 15,000 x 3.6048

     = $ 54,072

Present value of contest winning is $ 54,072

14.

Present value, PV and future value, FV are related as:

FV = PV x FVIF (r, n)

PV = FV/FVIF (r, n)

A)

r = rate of interest = 8 % p.a.

n = No. of periods = 12

FV = $ 40,000

PV = $ 40,000/ FVIF (8 %, 12)

     = $ 40,000/ 2.5182

     = $ 15,884.36

$ 15,884.36 needs to invest now to get $ 40,000 after 12 years @ 8 % discount rate

B)

If r = 12 %,

PV = $ 40,000/ FVIF (12 %, 12)

     = $ 40,000/ 3.8960

     = $ 10,266.94

$ 10,266.94 needs to invest now to get $ 40,000 after 12 years @ 12 % discount rate

15.

A)

FV = C x FVIFA(r, n)

FV = $ 40,000

r = rate of interest = 8 % p.a.

n = No. of periods = 12

C = Cash flow per period

$ 40,000 = C x FVIFA (8 %, 12)

     = C x 18.977

   C = $ 40,000/18.977

      = $ 2,107.81

$ 2,107.81 needs to invest annually to get $ 40,000 after 12 years @ 8 % discount rate.

B)

If r = 12 %,

$ 40,000 = C x FVIFA (12 %, 12)

     = C x 18.977

   C = $ 40,000/24.133

      = $ 1,657.48

$ 1,657.48 needs to invest annually to get $ 40,000 after 12 years @ 12 % discount rate.

16.

In order to compare the two alternatives we should compute the future value of annuity payments.

FV = C x FVIFA (r, n)

C = Cash flow per period = $ 14,000

r = rate of interest = 12 % p.a.

n = No. of periods = 10

FV = $ 14,000 x FVIFA (12 %, 10)

      = $ 14,000 x 17.549

      = $ 245,686

Future value of lump-sum = $ 200,000

As FV of annuity is more than lump-sum payment, annuity of $ 14,000 for 10 year should be preferred.