Inflation rate remains constant

2.1 Samuel invested an amount with ABC bank at an interest 12% p.a. compounded

His investment grew to R8450 at the end of 10 years. Determine the amount that Samuel initially invested. (3)

2.2 If the inflation rate remains at a constant 4,7 % p.a., what period of time will it take

for a certain amount to be worth half of the original amount. (3)

2.3 Lebogo buys a tractor for R𝑥. She plans to replace this tractor after 5 years.

The tractor depreciates by 20% p.a. according to the reducing balance method.

The price of a new tractor is expected to increase by 18% p.a.

She calculates that if she deposits R8 000 into a sinking fund at the end of each month, it would exactly provide for the shortfall 5 years from now when she has to pay for the new tractor. The bank offers 10% p.a. interest compounded monthly.

2.3.1 Calculate the scrap value of the tractor after 5 years, in terms of 𝑥? (1)

2.3.2 Determine the price of the new tractor after 5 years, in terms of 𝑥? (1)

 2.3.3 Calculate the amount accumulated in the sinking fund after 5 years. (4)

2.3.4 Determine the value of 𝑥, the price of the original tractor. . (4)

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