Question

1. You are thinking of investing £2000. You have found the following investment deals which seem good

The first one pays 4.50% annual interest compounded annually.

The second one pays 4.48% annual interest but compounded quarterly

The third one pays 4.45% annual interest but compounded monthly

1. Which one would be in your benefit to choose? How much money will you have after 3 years? (9 points)

2. Considering the above, explain how using both nominal and effective interest rates make financial decisions easier. (5 points, no more than 100 words)

2. Your company needs a new machine. Two companies are selling this machine in the market, their conditions are as below

Company A: The purchase of the new machine at a cost of £15,000. The purchase price includes maintenance for the first two years, but after that maintenance will cost £1,050 a year (payable at the end of each year).

The machine will have a useful life of five years, after which time it is estimated that it will have a scrap value of £4,000.

The expected income from the machine will be £1,500 at the end of the first year, £2,500 end of the second year, £3,500 end of the third year, £4,500 at the end of the fourth year, and £5,500 at the end of the fifth year.

Company B: The purchase of the new machine at a cost of £10,000. The purchase price includes maintenance for the first year, but after that maintenance will cost £1,000 a year (payable at the beginning of each year).

The machine will have a useful life of five years, after which time it is estimated that it will have a scrap value of £1,500.

The expected income from the machine will be £1000 at the end of the first year, £3000 each year at the end of the second, third and fourth years, and £5000 at the end of the fifth year

Assuming the discount rate is 4%, write a brief report advising the company on which contract will be more profitable and so whether it should accepted. Remember to take all costs and cash availability into consideration. Show any calculations you make in support of your recommendation. (14 points, no more than 500 words)

3. How confident are you about your advice and under what circumstances might it change? (5 points, no more than 100 words)

Answer 1

The formula for calculating the final amount with compound interest is

where P is the principal amount, r is the annual rate of interest in decimal form, n is the number of times that interest is compounded per unit time and t is the time for which the money is invested.

In our case, P is always equal to 2000 and the overall time is 3 years.

1st case :

r = 0.045, n = 1, t = 3

A = 2000 * (1+0.045)^3 = 2,282.33

2nd case :

r = 0.0448, n = 4 (as there are 4 quarters in a year), t = 3

A = 2000*(1+0.0448/4)^(4*3) = 2,285.99

3rd case :

r = 0.0445, n = 12 (monthly), t = 3

A = 2000*(1+0.0445/12)^{12*3} = 2,285.08

The second case has the Highest return amount. Hence, we should invest in it and we will get 2,285.99 pounds after 3 years.

B. Effective interest rate includes the effect of compounding in its calculation. Once it has been calculated, it can be seen as a nominal interest rate applied for the given amount of time. Hence, given a fixed duration, all that needs to be done is to compare the effective rate with the nominal one and see which is higher (the higher the better). Thus there is no need to do any calculation.

** Please post the second question as a new one.