Question

What was the interest rate, as a percent, given that the account was valued at $2748.79 at the end of year 5 and $2866.99 at the end of year 6?

a) 4.5%
b) 4.8%
c) 5.1%
d) 5.4%

Answer 1

The interest rate required to increase the account value from $2748.79 to $2866.99 in one year is approximately 4.3%, which is not listed among the options. The closest given choice is a.4.5%.

Step-by-step explanation:

The question asks for the interest rate that resulted in an account's value increasing from $2748.79 to $2866.99 across one year. To find the rate, we use the formula for simple interest: I = P × r × t, where I is the interest, P is the principal, r is the rate, and t is the time in years. Since the time frame is one year (t = 1), we can rearrange the formula to solve for the rate (r): r = I / (P × t). The interest earned is the change in account value, which is $2866.99 - $2748.79 = $118.20. The principal in this context is the initial amount, which is $2748.79.

To find the rate, we plug the values into the rearranged formula: r = $118.20 / ($2748.79 × 1), which when calculated gives an interest rate of approximately 0.043, or 4.3%. However, since 4.3% isn't an option, we check the closest available option which would be 4.5% (Option a).