Final answer:
To calculate how long it will take Esther to earn $275 in interest with $4250 at a 2% interest rate, we use the simple interest formula. The result is approximately 3.2 years when rounded to the nearest tenth.
Step-by-step explanation:
Esther wants to earn $275 in interest to be able to afford a new TV. She currently has $4250 in an account with a 2% interest rate. To calculate how long it would take her to reach her goal, we use the formula for simple interest, which is I = Prt, where I is the interest earned, P is the principal amount, r is the rate of interest per period, and t is the time in years. In this case, we need to solve for t. Plugging in the values, we get:
275 = 4250 × 0.02 × t
To solve for t, divide both sides by (4250 × 0.02):
t = 275 / (4250 × 0.02)
t ≈ 3.2353 years
Therefore, rounding to the nearest tenth, it would take Esther approximately 3.2 years to earn $275 in interest and reach her goal.