Final answer:
John initially borrowed R6968.64 from Tebogo. This was calculated using the simple interest formula by equating the total amount after five years with the sum of the principal and the interest accumulated over the period, considering the interest rate of 8.7% per year.
Step-by-step explanation:
To determine how much money John initially borrowed from Tebogo, we will use the formula for calculating simple interest, which is I = PRT, where I is the interest, P is the principal amount (the initial amount borrowed), R is the rate of interest per year, and T is the time in years. Given that the final amount (principal + interest) after five years is R10000.00 and the simple interest rate is 8,7% (or 0.087 as a decimal), we can write:
Total amount = Principal + Interest
Principal + Interest = Principal + (Principal * Rate * Time)
R10000.00 = P + (P * 0.087 * 5).
After combining like terms and simplifying, we get:
P(1 + 0.087 * 5) = R10000.00.
P(1 + 0.435) = R10000.00.
P(1.435) = R10000.00.
P = R10000.00 / 1.435.
Therefore, the initial amount borrowed (Principal, P) is R6968.64.