Question

George puts $200 into an account when the interest rate is 8 percent. Later he checks his balance and finds that he has a balance of about $272.10. How many years did he wait to check his balance?

a.3 years
b.3.5 years
c.4 years
d.4.5 years

Answer 1

The correct answer is option b. To calculate how many years it took for George's balance to reach $272.10, we can use the formula for compound interest and solve for time.

Step-by-step explanation:

To calculate how many years it took for George's balance to reach $272.10, we need to use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the ending balance, P is the principal amount (initial deposit), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, George initially deposited $200, the interest rate is 8% (or 0.08 as a decimal), and the balance is $272.10. Assuming that interest is compounded annually, we have:

$272.10 = $200(1 + 0.08/1)^(1*t)

Simplifying and solving for t, we get:

t = log(272.10/200) / log(1+0.08)

Calculating this gives us a value of approximately 3.5 years. Therefore, George waited about 3.5 years to check his balance (option b).