Question

Matthew invested $100 in a savings account earning 3% simple interest each year. Two years later, Jacob started a savings account with $100 at the same rate. Let t represent the number of years since Matthew invested his money. How does Jacob's savings compare to Matthew's savings at any time?

(a) Jacob's savings will always be greater.

(b) Matthew's savings will always be greater.

(c) Jacob's savings will exceed Matthew's savings after some time.

(d) Jacob's and Matthew's savings will always be equal.

Answer 1

Matthew's and Jacob's savings will always be equal.

Step-by-step explanation:

To compare Matthew's and Jacob's savings at any time, we need to consider the simple interest earned on their investments. Matthew invested $100 and earned 3% simple interest each year. So, his savings after t years can be calculated using the formula:

M = 100 + (100 * 0.03 * t)

Now, let's consider Jacob's savings. Like Matthew, he also started with $100 and earned 3% simple interest each year. So, Jacob's savings after t years can be calculated using the same formula:

J = 100 + (100 * 0.03 * t)

Since both Matthew and Jacob are earning the same interest rate and started with the same amount, their savings will always be equal at any given time. Therefore, the correct answer is option (d) Jacob's and Matthew's savings will always be equal.