One of your customers is having trouble paying her account. You agree to a repayment schedule of $300 per month. You charge 1% per month interest on late accounts. If the current balance is $2000, how long will it take to pay off the debt?
300( 1 - 1.01^-n)/.01 = 2000
300(1 - 1.01^-n) = 20
1 - 1.01^-n = 1/15
14/15 = 1.01^-n
ln both sides and use rules of logs
ln 14 - ln15 = -n ln 1.01
n = (ln 15 - ln 14)/ln 1.01
= 6.934
appr 7 months
of course I could have used log 15 etc.
and obtained the same result.
7 months
To determine how long it will take to pay off the debt, we need to calculate the number of months it will take for the customer to repay the balance of $2000.
First, let's calculate the interest charge for one month. Since the interest rate is 1% per month and the balance is $2000, the interest charge for one month is 1% of $2000, which is $20.
Now, let's determine how much of the monthly payment will go towards reducing the debt. To do this, we subtract the interest charge from the total monthly payment: $300 - $20 = $280.
Next, we divide the remaining debt by the amount of money that goes towards reducing the debt each month to find the number of months it will take to pay off the balance: $2000 / $280 = 7.14.
Since we can't have a partial month, we round up to the next month. Therefore, it will take approximately 8 months to pay off the debt.
Keep in mind that this calculation assumes the customer makes the agreed-upon monthly payments consistently and does not account for any additional charges or changes to the balance during the repayment period.