Your laptop died and you need a new one for work now. The one you need will cost $500. You do not have the cash in your checking account, so you decide to borrow the money from your savings account. You have $9,000 in your savings account gaining 3% interest per year. If you don’t replace the $500 in the savings account, how long will it take before the balance again reaches $9,000.
To calculate how long it will take for the balance to reach $9,000 again, we need to first calculate the amount of interest earned on the remaining balance after the $500 withdrawal.
Interest earned per year = $9,000 x 3% = $270
Remaining balance after withdrawal = $9,000 - $500 = $8,500
Therefore, the new balance after one year will be $8,500 + $270 = $8,770
We need to continue this calculation until the balance reaches $9,000 again.
$8,770 + $8,770 x 3% = $9,013.10 (balance after 1 year)
$9,013.10 + $9,013.10 x 3% = $9,274.46 (balance after 2 years)
$9,274.46 + $9,274.46 x 3% = $9,532.19 (balance after 3 years)
$9,532.19 + $9,532.19 x 3% = $9,786.85 (balance after 4 years)
It will take approximately 4 years for the balance to reach $9,000 again if the $500 is not replaced in the savings account.