Simple Interest

Exercise: Simple Interest

Questions for: Rate, Time, and Principal

An investor compares two simple interest savings accounts, Account X and Account Y, over different periods. Both accounts generate the exact same total interest amount at maturity. Account X started with a significantly larger principal deposit than Account Y. Given that both accounts yielded the same total simple interest and Account X had a larger principal than Account Y, which of the following statements *must* be true regarding their respective annual interest rates (R) and investment durations (T)?

A: The annual interest rate of Account X was lower than that of Account Y.

B: The investment duration for Account X was shorter than that for Account Y.

C: The product of the annual interest rate and investment duration for Account X was less than that for Account Y.

D: The sum of the annual interest rate and investment duration for Account X was less than that for Account Y.

Answer: C

1. The formula for simple interest is I = P * R * T, where I is interest, P is principal, R is annual rate, and T is time. 2. We are given that I_X = I_Y, so P_X * R_X * T_X = P_Y * R_Y * T_Y. 3. We are also given that P_X > P_Y. 4. For the equality P_X * (R_X * T_X) = P_Y * (R_Y * T_Y) to hold, if P_X is larger than P_Y, then the product (R_X * T_X) must be correspondingly smaller than the product (R_Y * T_Y). 5. Therefore, the product of the annual interest rate and investment duration for Account X (R_X * T_X) must be less than that for Account Y (R_Y * T_Y). Why others are wrong: A — The rate (R_X) could be higher or lower depending on the duration (T_X); it's not necessarily lower. B — The duration (T_X) could be shorter or longer depending on the rate (R_X); it's not necessarily shorter. D — The relationship between principal, rate, and time in simple interest is multiplicative, not additive; the sum does not necessarily follow this pattern.

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