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Economic Mathematics

You have to SHOW your work (show how you get the answers) to get credit. The answers to these problems are given to you on a separate file.

 

Below are the formulas for each type of loan and bonds. Use the respective formula regarding a respective question: for example, on questions regarding a simple loan use the simple loan formula, on questions regarding a fixed payment loan question use the fixed payment loan formula, and so on.

 

You also have to know the formulas for the test.

 

 

Future Value :

 

 

            FV= future value, PV= present value, i= interest rate, N= number of years.

.

 

Present Value:

 

FV= future value, PV= present value, i= interest rate, N= number of years.

 

 

Simple loan:

 

 

FV = future value, i = interest rate, n = number of years

 

 

Fixed payment loan:

 

 

FP = fixed payment, i = interest rate, n = number of years

 

 

Coupon bond:

 

P = price of bond, i = interest rate, n = number of years, c = coupon payment, and F = face value of the bond.

 

 

 

 

P = price of bond, C = coupon payment

 

 

 

F = face value, C = coupon payment

 

 

Discount Bond:

 

P = price of bond, i = interest rate, n = number of years, F = face value

 

 

Yield to maturity on a discount bond with less than a year of maturity:      

 

 

P = price of bond, F = Face value, G = number of days to maturity.

 

 

Yield on discount basis on a bond with less than a year of maturity:

 

 

 

P = price of bond, F = face value

 

 

Consol bond:

            P = price of bond, i = interest rate

 

 

 

 

 

 

Bring the answers to the following questions to Class

 

simple loan:

  1. End of ten years you will pay back $20,000. If I = 6% , how much is the loan amount now.

 

  1. If you borrowed $9900 at i = 10% to pay back at         the end of 15 years, how much money do you pay          back?

 

  1. You will receive $35,000 at the end of two Its present value is $20,000. The yield to maturity equals what?

 

fixed payment loan:

  1. i = 9%, loan = $15,000, 5 year loan. The fixed payment =___.

 

  1. The fixed payment = $7000,
    1. i= 9%, 3 years, loan =___

 

 

coupon bond:

  1. coupon payment = $100, face value = $6000,             i = 5%, 4 years, a) price of bond =___ b) coupon rate =___               c) current yield =____

 

  1. Coupon rate = 5%, face value = $12,000, i = 7%   a) price of bond for a) 1 year bond=___,   b) 2 year bond =____   c) 3 year bond =_____

 

  1. if i increases to 12% , what happens to each of the prices (in a) above.

 

discount bond (zero coupon bond):

 

  1. Face value = $20,000, price = $19,000, 1 year bond, ytm = _

 

  1. Face value = $20,000, price 19,000, 1 year bond , number of days to maturity = 90 days.   a) ytm =_______     b) yield on discount basis =___

 

  1. Face value = $15,000, 1 year bond, ytm = 6%, number of days to maturity = 180 days. A) price of bond =_______ b) yield on discount basis =___

 

 

console bond:

  1. i = 7%, price of bond = $15,000. coupon payment = _

 

  1. Coupon payment = $200,000 , i = 7%, price of bond =__

 

  1. Price of bond = $50,000 coupon payment = $300, ytm = __

 

Other Problems

 

  1. average interest rate equals 6%, You promised some one to pay her/him $10,000 at the end of 20 years. If the person insist to paid cash now how much should you give her/him now?

 

  1. Let’s say I am supposed to give you $12,000 at the end of 5 years, $16,000 at the end of 7 years, and another $15,000 at the end of 9 years. If the average rate of interest is 6% and you want to get your money now instead of waiting, how much should I give you?

 

  1. If the average rate of interest is 5%, and you want to receive $15,000 a year from a trust fund, how much money should you put in the trust fund?

 

  1. If the average rate of interest is 5%, and you deposit $2,000 a year during the coming 3 years how much money would you have at the end of the 3RD year?.

 

  1. If average interest rate is 7%, and tuition is currently $6,000 a year, how much would it be at the end of 3 years?

 

  1. You want your mother to receive $60,000 per year, if the average rate of interest is 5.5%, how much money should you put in a trust fund so your mother would get $60,000 per year?

 

 

 

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