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An amount of 5,000 is invested at a fixed rate of 8 per cent per annum. What amount will be the value of the investment in five years time, if the interest is compounded every six months?

Correct Answer: 7401.22

Explanation:

With slight modifications, the basic formula can be made to deal with compounding at intervals other than annually.


 


Since the compounding is done at six-monthly intervals, 4 per cent (half of 8 per cent) will be added to the value on each occasion.


 


Hence we use r = 0.04. Further, there will be ten additions of interest during the five years, and so n = 10. The formula now gives:


 


V = P(1 + r)10 = 5,000 x (1.04)10 = 7,401.22


 


Thus the value in this instance will be £7,401.22.


 


In a case such as this, the 8 per cent is called a nominal annual


 


rate, and we are actually referring to 4 per cent per six months.


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