Suppose you deposit $5,000 in a savings account that earns 3% annual interest. If you make no other withdrawals or deposits, how many years will it take the account balance to reach at least $6,000?
A) 10 years
B) 6 years
C) 7 years
D) 4 years
To find out how many years it will take for the account balance to reach at least $6,000, we can set up the following equation:
Principal + Interest = $6,000
The formula to calculate the interest is:
Interest = Principal * Rate * Time
We need to find the time (in years), so we can isolate the time variable in the equation.
$5,000 + ($5,000 * 0.03 * Time) = $6,000
Now, let's solve for Time:
$5,000 + $150 * Time = $6,000
$150 * Time = $6,000 - $5,000
$150 * Time = $1,000
Dividing both sides of the equation by $150, we get:
Time = $1,000 / $150
Time = 6.67
Therefore, it will take approximately 6.67 years for the account balance to reach $6,000.
However, since the time variable represents the number of years, we need to round the answer to the nearest whole number.
So, the correct answer is:
C) 7 years