Question

As the Fund Manager for Bank of Trinidad and Tobago Limited, you are to advise the following two (2) clients based on their respective financial situations. (Graded Manually)

a) Your best friend has asked to assist him in making the best investment out of the following options. Which would you advise him to choose and why? Show your workings to justify your response.

Option 1: $12,000 in 5 years’ time at 6 percent interest.

Option 2: $15,000 in 2 years’ time at 9 percent interest.

Option 3: $15,000 today. No strings attached.

Option4: $5,000 each year for 2 years at 7 percent interest compounded semi-annually.

b) Betty Kay has a contract in which she will receive the following payment for the next 5 year: $1,000, $2,000, $3,000, $4,000 and $5,000. She will then receive an annuity of $8,500 a year for the end of the 6th through the end of the 15th year. She is offered a $30,000 to cancel the contract. If the payments are discounted at 14 percent should she cancel the contract? Show all workings.

Answer 1

a. The present value is computed as follows:

= Future value / (1 + r)ⁿ

Option 1 value will be as follows:

= $ 12,000 / 1.06⁵

= $ 8,967

Option 2 value will be as follows:

= $ 15,000 / 1.09²

= $ 12,625

Option 3 value will be as follows:

= $ 15,000 (Since the money is received today only)

Option 4 value will be as follows:

r will be as follows:

= 7% / 2 (Since the interest is compounded semi annually)

= 3.5% or 0.035

n will be as follows:

= 2 x 2 (Since the interest is compounded semi annually)

= 4

So, the amount will be as follows:

= $ 5,000 / 1.035 + $ 5,000 / 1.035² + $ 5,000 / 1.035³ + $ 5,000 / 1.035⁴

= $ 18,365.40

b. The value is computed as follows:

= Future value / (1 + r)ⁿ

= $ 1,000 / 1.14¹ + $ 2,000 / 1.14² + $ 3,000 / 1.14³ + $ 4,000 / 1.14⁴ + $ 5,000 / 1.14⁵ + $ 8,500 / 1.14⁶ +  $ 8,500 / 1.14⁷ +  $ 8,500 / 1.14⁸ +  $ 8,500 / 1.14⁹ +  $ 8,500 / 1.14¹⁰ +  $ 8,500 / 1.14¹¹ +  $ 8,500 / 1.14¹² +  $ 8,500 / 1.14¹³ +  $ 8,500 / 1.14¹⁴ +  $ 8,500 / 1.14¹⁵

= $ 32,433.45

Since the present value is more than $ 30,000, hence she shall not cancel the contract

Do ask in case of any doubts.