Question

Joyce has just contracted to sell a small parcel of land that she inherited a few years ago. The buyer is willing to pay R28 000 at the closing of the transaction or will pay the amounts shown in the following table at the beginning of each of the next five years. Because Joyce doesn’t really need the money today, she plans to let it accumulate in an account that earns 10% annual interest. Given her desire to buy a house at the end of five years after closing on the sale of the lot, she decides to choose the payment alternative – R28 000 lump sum or mixed stream of payments in the following table – that provides the highest future value at the end of five years.

Beginning of Year (t)	Cash Flows (in Rands)
1	3 000
2	6 000
3	9 000
4	12 000
5	15 000

2.1. What is the future value of the lump sum at the end of Year 5? [3]

2.2. What is the future value of the mixed stream at the end of Year 5? [4]

2.3. Based on your findings in parts (2.1) and (2.2), which alternative should Joyce take? [2]

2.4. If Joyce could earn 15% rather than 10% on the funds, would your recommendation in part (2.3) change? Explain.

Answer 1

Based on the results, Joyce should take 28,000 today and invest it at 10%.

If rate was 15%

Clearly, the future value from installement is greater than lump sum payment in this case also.

So, no change is recommended.

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