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?
To find out how many years it will take the account balance to reach at least $6,000, we need to determine the interest earned each year.
The formula for calculating interest is:
Interest = Principal * Rate
In this case, the principal is $5,000 and the rate is 3%.
Interest = $5,000 * 0.03 = $150
Now, let's calculate how many years it will take for the balance to reach $6,000.
Balance after one year = Principal + Interest = $5,000 + $150 = $5,150
Balance after two years = Principal + Interest = $5,150 + $150 = $5,300
Balance after three years = Principal + Interest = $5,300 + $150 = $5,450
Balance after four years = Principal + Interest = $5,450 + $150 = $5,600
Balance after five years = Principal + Interest = $5,600 + $150 = $5,750
At this point, the balance is still less than $6,000.
Balance after six years = Principal + Interest = $5,750 + $150 = $5,900
Finally,
Balance after seven years = Principal + Interest = $5,900 + $150 = $6,050
After seven years, the account balance will reach at least $6,000.
Therefore, it will take seven years for the account balance to reach at least $6,000.