Question

Gertrude deposits $10,000 in a bank. During the first year, the bank credits an annual effective rate of interest i. During the second year, the bank credits an annual effective rate of interest, (i−5%). At the end of two years, she has 12,093.75 in the bank. What would Gertrude have in the bank at the end of three years, if the annual effective rate of interest were (i + 9%) for each of the three years?

Answer 1

The question involves determining the bank balance after three years with compound interest, but to provide a direct answer, the effective annual interest rate, 'i', must first be calculated from the initial conditions. With that rate, we could calculate the balance after three years.

Step-by-step explanation:

The subject of this question is compound interest, which is a concept in mathematics that describes how investments grow over time when the interest earned is reinvested to earn additional interest. Gertrude deposited $10,000 in a bank account that credited different effective annual interest rates over two years, resulting in a balance of $12,093.75 at the end of the second year. To find out the balance at the end of three years with an annual effective rate of interest of (i + 9%) for each of the three years, we can use the compound interest formula.

Step-by-Step Calculation:

1. Calculate the effective annual interest rate for the first two years using the given final balance and initial deposit.
2. Apply the calculated interest rate with an additional 9% for the third year.
3. Calculate the new balance after the third year using the compound interest formula.

To provide an accurate answer, we need the effective annual interest rate for the first year which was not provided. However, the process described here outlines how one would proceed if the initial interest rate were known.