Final answer:
The subject is comparing 3% simple interest (Option B) with 3% compound interest (Option F). Simple interest on $100 over three years is $9, while compound interest gives $15.76, showing that compound interest yields more over time, especially with larger sums and longer terms.
Step-by-step explanation:
To compare a simple interest savings option with a compound interest savings option, let's choose Option B which earns 3% simple interest per year, and Option F which earns 3% compound interest per year. The formula for calculating simple interest is Interest = Principal × Rate × Time. For example, if we start with $100 at a simple interest rate of 3% for three years, the interest earned would be $100 × 0.03 × 3, which equals $9.
Compound interest differs in that it is calculated not only on the principal amount but also on the accumulated interest of previous periods. Assuming the same initial amount, rate, and duration for compound interest, the first year would yield the same amount of $3. However, in the second year, you would earn interest on $103, and so on. Over time, this leads to more interest earned compared to simple interest. As noted earlier, after three years, the total with compound interest is $115.76, reflecting a total compound interest of $15.76, which is $0.76 more than with simple interest. This may seem like a small difference with $100 over three years but is significantly greater with larger sums of money and over longer periods of time.