Question

Sally currently has an account balance of $991.41. Her initial deposit on the account was $540, and it earned $4.40 in simple interest. How long has Sally had the account?

a) 1 year
b) 2 years
c) 3 years
d) 4 years

Answer 1

To determine how long Sally has had the account, we divide the interest earned by the initial deposit to find the annual interest rate. Then, we use the formula for compound interest and logarithms to solve for the number of years. In this case, Sally has had the account for approximately 4 years.

Step-by-step explanation:

To find out how long Sally has had the account, we need to determine the annual interest rate. We can do this by dividing the interest earned by the initial deposit and the number of years it has been held. In this case, the annual interest rate is $4.40 / $540 = 0.0081481. Now, we can use the formula for compound interest to calculate the number of years:

$991.41 = $540(1 + 0.0081481)^t

Dividing both sides of the equation by $540, we get:

1.835 = (1.0081481)^t

Taking the logarithm of both sides, we can solve for t:

t = log(1.835) / log(1.0081481)

Using a calculator, we find that t ≈ 3.0225. Since we are looking for the number of years, we can round t up to 4 years.