Final answer:
The initial amount of money John borrowed from Tebogo was approximately R6,968.29. This was calculated using the formula for simple interest and solving for the principal by rearranging the formula and substituting the given values.
Step-by-step explanation:
To calculate the initial amount of money John borrowed from Tebogo at a simple interest rate of 8.7% per year, we need to use the formula for simple interest: Interest = Principal × rate × time. Given that after five years John owes Tebogo R10,000, we can assume this is the total amount of the principal plus the interest accrued over the five years.
First, we rearrange the simple interest formula to solve for the principal: Principal = Interest / (rate × time). To find the interest, subtract the principal from the total amount owed:
Total owed = Principal + Interest
10,000 = Principal + Interest
Interest = 10,000 - Principal
Then we substitute the values into the rearranged formula:
Principal = (10,000 - Principal) / (0.087 × 5).
Since we have 'Principal' on both sides of the equation, we need to solve for it algebraically. Let's call the initial principal amount 'P'. Now we have:
10,000 = P + (P × 0.087 × 5)
10,000 = P (1 + 0.087 × 5)
10,000 = P (1 + 0.435)
10,000 = P × 1.435
To find 'P', we divide both sides by 1.435:
P = 10,000 / 1.435
P ≈ R6,968.29
Therefore, the initial amount John borrowed was approximately R6,968.29.