Sandy made several investments. She bought 850 shares of a company's stock for $8.40/share, she bought a bond with a face value of $3500 and a coupon rate of 7%, and she invested $4300 into a fund that is expected to grow by 3.5% per year.

a. Sandy pays a broker a commission of $14 to buy and sell stock. After one year, Sandy sold all her shares, when they were worth $9.15/share. What was her net gain or loss? Be sure to state whether it is a gain or loss. Show your work

b. The bond Sandy purchased will mature in 10 years. How much interest will she receive semiannually?

c. How long will it take the fund she invested in to be worth $7,000?

d. Sandy's gross annual income is $50,850. She is paid biweekly and has a 4.5% deducts from her paycheck for her 403 (b). Her employer matches her deduction, up to 4%. How much is deposited into Sandy's 403 (b) each payday?

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Question

Taryn Prince

Mathematics

17 September, 15:30

Sandy made several investments. She bought 850 shares of a company's stock for $8.40/share, she bought a bond with a face value of $3500 and a coupon rate of 7%, and she invested $4300 into a fund that is expected to grow by 3.5% per year.

a. Sandy pays a broker a commission of $14 to buy and sell stock. After one year, Sandy sold all her shares, when they were worth $9.15/share. What was her net gain or loss? Be sure to state whether it is a gain or loss. Show your work

b. The bond Sandy purchased will mature in 10 years. How much interest will she receive semiannually?

c. How long will it take the fund she invested in to be worth $7,000?

d. Sandy's gross annual income is $50,850. She is paid biweekly and has a 4.5% deducts from her paycheck for her 403 (b). Her employer matches her deduction, up to 4%. How much is deposited into Sandy's 403 (b) each payday?

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Answers (1)

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Troy Farrell · Answer 1

a.$609.5

b.$122.5

c. 14.16 years

d.$ 180.09

Step-by-step explanation:

The cost of the shares = (850*$8.40) + $14=$7154

proceeds from sale of shares = (850*$9.15) - $14=$7763.5

Gain on sale of shares=$7763.5 - $7154=$609.5

The interest receivable semiannually=$3500*7%*6/12=$122.5

The length of time it would take for the fund to worth $7,000 can be derived from future value formula

FV=PV * (1+r) ^n

FV is $7000

PV is $4,300

r is the growth rate per year of 3.5%

n is the not known

7000=4300 * (1+0.035) ^n

7000/4300=1.035^n

1.627906977 = 1.035^n

take log of both sides

ln 1.627906977 = n ln1.035

n=ln 1.627906977 / ln 1.035=14.16 years

biweekly gross income = ($50,850/12*2) = $2118.75

(4%+4.5%) * 2118.75 = $ 180.09