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

Question

Quizplus · Accepted Answer

Using the formula for compound interest:

A = P(1+r/n)^(nt)

where A is the balance after time t, P is the initial investment, r is the annual interest rate, n is the number of times compounded in a year, and t is the time in years.

Given:
P = $200
r = 8% = 0.08
A = $272.10

Let's assume interest is compounded annually (n=1).

$272.10 = $200(1+0.08)^t
1.3605 = (1.08)^t
ln(1.3605) = ln(1.08)^t
t= ln(1.3605) /ln(1.08)
t= 4.00 years (rounded to two decimal places)

Therefore, George waited for 4 years. The answer is C.

George Puts $200 into an Account When the Interest Rate