Final answer:
The student is asked to calculate and compare the interest earned using simple and compound interest on an investment of R105,000 over 8 years at a 10% interest rate. The simple interest can be calculated with the formula Interest = Principal × Rate × Time, and compound interest would be calculated using the formula A = P(1 + r/n)^(nt). The difference between the two types of interest will demonstrate the impact of compound interest over the long term.
Step-by-step explanation:
The question asks to determine the difference in interest earned on an investment of R105,000 at a 10% annual interest rate over 8 years, comparing simple interest and compound interest. To find the interest earned using simple interest, you would use the formula Interest = Principal × Rate × Time, which in this case would be Interest = R105,000 × 0.10 × 8. The total simple interest earned would be R84,000.
To calculate compound interest, you use the formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for. Assuming the interest is compounded annually (n=1), the formula for this scenario is A = R105,000(1 + 0.10)^8. The future value using compound interest would then be calculated and the interest earned would be the difference between the future value and the principal.
The difference in interest between simple and compound interest is the compound interest minus the simple interest, indicating that compound interest can significantly increase earnings over time, especially with larger sums of money and longer investment periods.