Financial Math Answers

Suppose the short-run cost function of Tyrell Corporation is 𝒄 = 𝟓𝟎𝟎𝟎 + 𝟏𝟎𝟎𝒒 + 𝟖𝒒^𝟐. 

a.  Find the level/s of  that satisfies/satisfy the first-order and second-order conditions for the minimisation

of Tyrell’s average cost (𝒂𝒄). [4]

Show that 𝒂𝒄 equals marginal cost (𝒎𝒄) at the level/s of  obtained in (a). [2

Jennifer opted for the plan that will pay her $ 52,000 annually for 15 years. The cash will be paid at the end of each year

Required

A. Assuming that the interest will remain at 6.8 % constant over the whole period , how much will the insurance company disburse at the end of the 15 years of annuity payment to Jennifer? [ordinary annuity]

B. If the payment of the cash flow is done in the beginning of the period , what will be the sum for the insurance company will disburse? [interest rate changes to 7.5%]

C. If Jennifer is supposed to invest a sum at the beginning of the retirement in the annuity fund of the insurance , calculate the sum she has to give to the company if

a. Payment is received at the end of each period and the interest rate is 4.8%

b. Payment is done at the beginning of each period and the interest rate is 5.8%

[ Annual payment = $52,000 and period is 15 years]

Mr LEO’s father has made a will to give him an amount of $500,000 in 10 years .So Leo wants to borrow an amount from the bank to set up a fashion boutique in the nearest town. The business planner told him that he does not expect the present discount rate to change in these 10 years. The following information is given regarding the discount rate

  GDP growth of the country

1.2%

Beta

1.8

Index in January 2020

16,570

Index in December 2020

17,590

Inflation

2.5%

 REQUIRED

How much should he borrow from the bank now if he is planning to pay back the loan with the money he will get in 10 years of business return?

Suppose Maria gets R13240.10 after investing a lump for 5 years.The bank quoted 11.5% simple interest.How much did Maria invest at the beginning?

A firm estimates that it can sell Q units of its product with an advertising expenditure of x thousand dollars where

Q = Q(x)=x² + 600x + 25

i) Over what level of advertising expenditure is the number of units of

product sold increasing?

ii) Over what level of advertising expenditure is the number of units of product sold decreasing?

a. Where do we use Present Value. Give three examples and explain how PV is used in these fields

Compare with examples the difference between compounding and discounting.

Melanie is deciding which of the two long term savings plan to choose for investing $9000: 6.2% per annum, compounding semi-annually, or 5.75% per annum compounded quarterly. If she plans to leave the money in the plan of 8 years, which is the better option?

A home was bought with a 20% down payment of R177 175,00. The balance was financed for 20 years at

9,4% interest per annum, compounded semi-annually. Find the size of the half-yearly payments for the loan.

a. John won a lottery worth $145,000 and she is expecting to buy a business in five years from now. He has been told by the bank that he would need about $350,000 to set the business in the future. What percentage of the business can be funded by the money from the lottery in 5 years from now. [Assume that interest will remain 7.7% unchanged. ]

b. Mr LEO’s father has made a will to give him an amount of $500,000 in 10 years .So Leo wants to borrow an amount from the bank to set up a fashion boutique in the nearest town. The business planner told him that he does not expect the present discount rate to change in these 10 years. The following information is given regarding the discount rate

  GDP growth of the country

1.2%

Beta

1.8

Index in January 2020

16,570

Index in December 2020

17,590

Inflation

2.5%

 REQUIRED

How much should he borrow from the bank now if he is planning to pay back the loan with the money he will get in 10 years of business return?