At what annual simple interest 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?
Let x be the annual simple interest for the investment of R96 for 1 year and 5 months.
The interest earned on R75 invested at 10% per annum for 1 year is calculated as:
Interest = Principal x Rate x Time
Interest = 75 x 0.10 x 1
Interest = 7.5
For the investment of R96 for 1 year and 5 months, the interest earned should also be 7.5.
Time in years for 1 year and 5 months = 1 + 5/12 = 1.42 years
Interest = Principal x Rate x Time
7.5 = 96 x x x 1.42
7.5 = 136.32x
x = 7.5 / 136.32
x ≈ 0.055
Therefore, the annual simple interest for R96 to produce the same interest earned as R75 at 10% per annum for 1 year is approximately 5.5%.