Final answer:
Michael invested his money at 7 ¼% annual simple interest for 3.5 years to achieve the maturity value of $12,537.50. This was determined using the simple interest formula.
Step-by-step explanation:
To calculate how long Michael invested his money at 7 ¼% annual simple interest to reach a maturity value of $12,537.50, we use the simple interest formula I = Prt, where I is the interest earned, P is the principal amount invested, r is the annual interest rate (as a decimal), and t is the time in years.
First, we find the total interest earned by subtracting the principal from the maturity value: $12,537.50 - $10,000 = $2,537.50.
Then, we convert the annual interest rate from a percentage to a decimal by dividing by 100: 7 ¼% = 0.0725.
Now we can use the simple interest formula to solve for time, t.
I = PrtI = $2,537.50, P = $10,000, r = 0.0725
To find t, we rearrange the formula to t = I / (Pr) and plug in the values:
t = $2,537.50 / ($10,000 × 0.0725)t = 3.5 years
Therefore, Michael invested the money for 3.5 years.