Final answer:
To find which account has the greater principal, use the simple interest formula to solve for the principal. With $50 in interest for Account A at 2% and $21 in interest for Account B at 3% over 21 months, Account A has the greater principal because it requires a larger initial sum to accumulate $50 at the lower interest rate.
Step-by-step explanation:
The student's question concerns comparing two separate accounts with different simple interest rates to determine which account has the greater principal. The simple interest formula is Interest = Principal × Rate × Time, where the principal is the initial amount deposited, the rate is the annual interest rate, and the time is the period for which the money is invested or borrowed.
To solve this problem, we rearrange the formula to solve for the principal: Principal = Interest ÷ (Rate × Time). Since Account A received $50 in interest at a rate of 2% over 21 months, and Account B received $21 in interest at a rate of 3% over the same period, we can calculate the principal for each:
- Principal A = $50 ÷ (0.02 × 21/12)
- Principal B = $21 ÷ (0.03 × 21/12)
Calculating the above, Principal A will be greater than Principal B, thus Account A has the greater principal because more money is needed to generate $50 at a lower interest rate compared to what is needed to generate $21 at a higher rate.