Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

MTH120

Questions

Assignment 1

1. The effective rate of discount per annum is 5%. Calculate

(a) the equivalent force of interest;                                                                                                  [3] (b) the equivalent rate of interest per annum convertible monthly;                                                [2]

(c) the equivalent rate of discount per annum convertible monthly.                                               [2] [Total 6]

2. The force of interest δ(t) is given by the formula

δ(t) = 

(a)  Calculate the present value of a unit sum of money due at time t = 20.                                  [5] (b)  Calculate the equivalent constant force of interest from t = 0 to t = 20.                                  [2]

(c)  Calculate the present value at time t = 0 of a continuous payment stream payable at a rate of e −o.o6p  from time t = 4 to time t = 8.                                                                                         [4]

[Total 11]

3.   (a)  Show that

 =  + i                                                                [4]

(b) Find the corresponding versions of the same identity for a  n((夕)) , n((夕))  and an .                              [7] [Total 11]

4. A loan of f60,000 was granted on 1 July 1998. The loan is repayable by an annuity payable quarterly in arrear for 20 years.  The amount of the quarterly repayment increases by f100 after every four years. The repayments were calculated using a rate of interest of 8% per annum convertible quarterly.

(a)  Show that the initial quarterly repayment is f1,370.41.                                                           [5] (b)  Calculate the amount of capital repaid that was included in the payment made on 1 January 1999.                                                                                                                                            [4] (c)  Calculate the amount of capital outstanding after the quarterly repayment due on 1 July 2011 has been made.                                                                                                                           [3]

[Total 12]

5. A loan of nominal amount f100,000 was issued on 1 April 2011 bearing interest payable half-yearly in arrear at a rate of 6% per annum. The loan is to be redeemed with a capital payment of f105 per f100 nominal on any coupon date between 20 and 25 years after the date of issue, inclusive, with the date of redemption being at the option of the borrower.

An investor who is liable to income tax at 20% and capital gains tax of 35% wishes to purchase the entire loan on 1 June 2011 at a price which ensures that the investor achieves a net effective yield of at least 5% per annum.

(a) Determine whether the investor would make a capital gain if the investment is held until re- demption.                                                                                                                                    [3]

(b) Explain how your answer to (a) influences the assumptions made in calculating the price the

investor should pay.

(c)  Calculate the maximum price the investor should

pay.

[2] [5]

[Total 10]