Two friends, Kuda and Thabo, each want to invest R5 000 for four years. Kuda invests his money in an account that pays simple interest at 8.3% per annum. At the end of four years, he will receive a bonus of exactly 4% of the accumulated amount. Thabo invests his money in an account that pays interest at 8.1% p.a., compounded monthly. Whose investment will yield a better return at the end of four years? Justify your answer with appropriate calculations.

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Two friends, Kuda and Thabo, each want to invest R5 000 for four years - NSC Mathematics - Question 8 - 2019 - Paper 1

Question 8

Two friends, Kuda and Thabo, each want to invest R5 000 for four years. Kuda invests his money in an account that pays simple interest at 8.3% per annum. At the end ... show full transcript

Worked Solution & Example Answer:Two friends, Kuda and Thabo, each want to invest R5 000 for four years - NSC Mathematics - Question 8 - 2019 - Paper 1

Step 1

Calculate Kuda's Total Amount

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Answer

To find Kuda's total amount after four years, we first calculate the simple interest:

Simple Interest (SI) formula: $SI = \frac{P \times r \times t}{100}$ Where:

P = principal amount = R5000
r = interest rate = 8.3%
t = time in years = 4

Thus, $SI = \frac{5000 \times 8.3 \times 4}{100} = R1660$

Now, we calculate the total amount after four years: $\text{Total Amount} = P + SI = R5000 + R1660 = R6660$

Adding the bonus of 4% on R6660: $\text{Bonus} = \frac{4}{100} \times 6660 = R266.40$

Final amount Kuda will receive: $\text{Final Amount} = R6660 + R266.40 = R6926.40$

Step 2

Calculate Thabo's Total Amount

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Answer

Thabo's investment earns interest compounded monthly. The formula for compound interest is:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$ Where:

A = the future value of the investment/loan, including interest
P = principal investment amount (R5000)
r = annual interest rate (decimal) = 8.1% = 0.081
n = number of times that interest is compounded per year = 12
t = number of years the money is invested or borrowed = 4

Plugging in the values: $A = 5000 \left(1 + \frac{0.081}{12}\right)^{12 \times 4}$ $A = 5000 \left(1 + 0.00675\right)^{48}$ $A = 5000 \left(1.00675\right)^{48}$ Using a calculator: $A \approx 5000 \times 1.348713 = R6743.57$

Step 3

Compare Kuda and Thabo's Investments

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Answer

Kuda's final amount is R6926.40 and Thabo's final amount is R6743.57.

Therefore, Kuda's investment yields a better return at the end of four years.

Two friends, Kuda and Thabo, each want to invest R5 000 for four years - NSC Mathematics - Question 8 - 2019 - Paper 1

Worked Solution & Example Answer:Two friends, Kuda and Thabo, each want to invest R5 000 for four years - NSC Mathematics - Question 8 - 2019 - Paper 1

Calculate Kuda's Total Amount

Calculate Thabo's Total Amount

Compare Kuda and Thabo's Investments

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