Final answer:
To determine the principal, divide the interest earned by the product of the annual interest rate as a decimal and the time in years. The calculation will yield the initial amount invested, which then can be rounded to the nearest dollar.
Step-by-step explanation:
To calculate the principal amount invested, given the interest earned and the interest rate, you can rearrange the simple interest formula: Interest = Principal × Rate × Time. In this case, you earned $246.75 in interest at a rate of 3.5% over 18 months. To find the principal (the initial investment), divide the interest earned by the product of the interest rate and the time period (in years).
First, convert the interest rate from a percentage to a decimal: 3.5% = 0.035. Next, convert the time period to years by dividing the number of months by 12: 18 months ÷ 12 = 1.5 years.
Now, use the formula to find the principal: Principal = Interest ÷ (Rate × Time) = $246.75 ÷ (0.035 × 1.5). When you calculate this, it will give you the amount invested. You can then round this number to the nearest dollar.