Question

Hector puts $150 into an account when the interest rate is 4 percent. later he checks his balance and finds he has about $168.73. how long did hector wait to check his balance?

Answer 1

Hector waited approximately 2.935 years for his bank balance to increase from $150 to $168.73 at an annual interest rate of 4% when compounded annually.

Step-by-step explanation:

To determine how long Hector needed to wait for his balance to increase from $150 to $168.73 with an annual interest rate of 4%, we will use the formula for compound interest which is A = P(1 + r/n)(nt), where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount.
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for in years.

Since the compounding frequency is not mentioned, we'll assume it is compounded once a year (n=1). We need to solve for t given:
P = $150
r = 0.04 (4% written in decimal form)
A = $168.73
The equation thus becomes $168.73 = $150(1 + 0.04)t.

To solve for t, we will first divide both sides of the equation by $150 to isolate the growth factor:
$168.73 / $150 = (1 + 0.04)t

Now solving for t, we'll use logarithms:
t = log(168.73/150) / log(1.04)

Using a calculator to find the value of t gives:
t ≈ 2.935

Therefore, Hector waited approximately 2.935 years to check his balance.

Answer 2

3 years, 1 month, and 15 days.

Find time by using the formula

(I = P · i · t) where I is interest, P is total principal, i is rate of

interest per year, and t is total time in years.

In this problem I = $18.73 , P = $150 and i = 4%