Question 3 (9 marks) 16 minutes You are planning to take a holiday in Mauritius

Question

Question 3 (9 marks) 16 minutes You are planning to take a holiday in Mauritius when your current savings of NS 10 000 reach a) If you take your holiday at the end of five years from now, what is the annual rate of b) If you are willing to wait seven years before taking your holiday, what annual rate of N$ 20 000. interest will you have to earn on your savings account? (3 marks) (3 marks) interest would be necessary on your savings ifyou can earn 7% per year compounded semi-annuny on your savings account, how c) long wil it take before you have adequate funds to take your holiday? (3 marks)

Explanation / Answer

In order to solve this question, we need to use the time value of money equation: FV = PV * (1 + r)n

Part a) FV = NS 20,000, PV = NS 10,000, n = 5 years, r = ?

Substituting these values in time value of money function above,

20000 = 10000 * (1 + r)5

2 = (1 + r)5

(1 + r) = 1.1487

r = 14.87%

Part b) FV = NS 20,000, PV = NS 10,000, n = 7 years, r = ?

Substituting these values in time value of money function above,

20000 = 10000 * (1 + r)7

2 = (1 + r)7

(1 + r) = 1.1041

r = 10.41%

Part c) FV = NS 20,000, PV = NS 10,000, r = 7% per year --> 3.5% semi-annually, n = ?

Substituting these values in time value of money function above,

20000 = 10000 * (1 + 0.035)n

2 = (1 + 0.035)n

Taking natutal log on both sides, we get

LN (2) = n LN(1.035)

n = 0.6931/0.0344

n = 20.15 semi-annual periods --> 10.08 years

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