Final answer:
To earn $100 in interest over 14 months at a 2.5% simple interest rate, one would need to invest roughly $3428.57.
Step-by-step explanation:
To determine how much one should invest to earn $100 interest at a 2.5% simple interest rate over 14 months, we can use the formula for simple interest: I = P × r × t, ( where I is the interest earned, P is the principal (the initial amount invested), r is the annual interest rate (in decimal form), and t is the time the money is invested (in years).
Since we want to earn $100, we set I = $100, r = 0.025 (2.5% as a decimal), and t = 14/12 years (because there are 12 months in a year).
Then we rearrange the formula to solve for the principal P:
P = I / (r × t).
Plugging in the values we get:
P = $100 / (0.025 × (14/12))
= $100 / (0.025 × 1.1667)
= $100 / 0.02917
≈ $3428.57.
Therefore, one would need to invest approximately $3428.57 at a 2.5% simple interest rate to earn $100 in interest over 14 months.