Applications of Mathematics in Finance and Investment Assignment -

Q1. An investor deposits £100 into a savings account at the beginning of each month over the next 14 years. The interest rate offered is 6% per annum effective in the first ten years and 6% per annum convertible monthly for the remaining four years.

Calculate the accumulated value of the savings at the end of the 14- year period.

Q2. The force of interest at time t, measured in years, is given by the formula:

0.04 0.003t² 0 t 5

t 0.01 0.03t 5 t

(a) Calculate the present value of £10,000 due at time t = 7.

(b) Calculate the constant annual rate of discount, which would lead to the same present value as that in (a) being obtained.

(c) Calculate the present value at time t = 0 of a continuous payment stream made at the rate of 100e0.02 t 0.015t2 per annum, received from time t = 5 to t = 10.

Q3. A fund had a value of £100 million on 1st January 2015. A net cash flow of £2.2 million was received on 1st July 2016 and a further net cash flow of £3.4 million was received on 1st July 2017. Immediately before the first cash flow, the fund had a value of £116 million and immediately before receipt of the second cash flow, the fund had a value of £160 million. The value of the fund on 31st December 2017 was £180 million.

For the period between 1^st January 2015 and 31st December 2017, calculate the following:

(a) The money weighted rate of return (MWRR) earned on the fund;

(b) The time weighted rate of return earned on the fund.

Q4. The n-year spot rate of interest y_n is given by:

y_n 0.045 n/1000 for n = 1, 2, 3 and 4

Calculate, to 6 significant figures:

(a) All possible one-year forward rates;

(b) All possible two-year and three-year forward rates;

(c) The price at time t = 0, of a unit zero coupon bond with term 3 years;

(d) The implied 4-year par yield.

Note - Show all working out. Show what formulas was used in each question.