**Instructions to students:**

**All questions are compulsory.**

**Materials:**

Dictionaries are not permitted.

Actuarial Tables.

## TASK: AS1201 Financial & Investment Mathematics Assignment

**Question 1**

A 3-month deposit account pays a rate of interest of 5% per annum convertible half-yearly.

Calculate the simple rate of discount per annum which is equivalent to the above investment over the 3-month period. **(3 marks)**

**Question 2**

An investor pays £1,200 per annum into a savings account for 10 years, and increases the payments to £1,500 per annum for the next 5 years. The payments are made annually in advance.

Calculate the accumulated amount in the savings account at the end of the 15 years if the investor achieves a yield of 6% per annum convertible half-yearly on her investment.**(4 marks)**

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**Question 3: **

The force of interest is given by:

*δ *( *T* ) = 0.03 + 0.001*T* + 0.0005*T* ^{2} FOR 0 ≤ *T* ≤ 12

i)Calculate the accumulation at time 12 of an initial investment of £100 at time 0 plus a further investment of £100 at time 6.**(3 marks)**

ii)Calculate the equivalent constant force of interest earned on the transaction.(**4 marks)****[Total 7 marks]**

**Question 4: ****AS1201 Financial & Investment Mathematics Assignment**

A car leasing company purchases cars from a manufacturer and immediately rents them out to clients on a four-year contract.

The current purchase price of each car is £20,000 and the company expects that the sale price of each car at the end of the contract will be £8,000. The rental income is payable continuously throughout the four-year period and increases by £1,000 at the end of each year.

Calculate the initial annual rental rate the car hire company must charge in order to achieve an internal rate of return of 10% per annum.**(5 marks)**

**Question 5**

A businessman is buying a mine for an initial investment of £1,000,000. A further investment of £500,000 will be required at the start of the second year.

Net revenue from the mine will be received continuously from the start of the first year until the end of the twentieth year, when the minerals will be exhausted. The initial rate of net revenue is £120,000, and this is assumed to grow continuously at a rate of 5% per annum effective.

i)Calculate the net present value of the project at an effective rate of interest of 8% per annum.**(5 marks)**

ii)Calculate the discounted payback period of the project at an effective rate of interest of 8% per annum.**(4 marks)[Total 9 marks]**

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