At what annual simple interest rate should R96 be invested for 1 year and 5 months, so as to produce the same interest earned if R75 was invested at 10% per annum for 1 year?
First, we need to determine the interest earned on the R75 investment at 10% per annum for 1 year:
Interest = (Principal x Rate x Time)
Interest = (R75 x 10% x 1 year)
Interest = R7.50
Now we need to find the simple interest rate that will produce the same interest earned on R96 for 1 year and 5 months (or 1.42 years):
Interest = (Principal x Rate x Time)
R7.50 = (R96 x Rate x 1.42 years)
Rate = R7.50 / (R96 x 1.42 years)
Rate = 0.056 or 5.6%
Therefore, R96 should be invested at an annual simple interest rate of 5.6% for 1 year and 5 months to produce the same interest earned as R75 invested at 10% per annum for 1 year.