Question

One of your customers is delinquent on his accounts payable balance. You’ve mutually agreed to a repayment schedule of $750 per month. You will charge 1.9 percent per month interest on the overdue balance. If the current balance is $18,000, how long will it take for the account to be paid off? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Months for account to be paid off months

Answer 1

32.34 months

Step-by-step explanation:

A = monthly payment amount P = loan amount i = monthly interest rate n = total number of payments.

A = 750, P = 18000 i = 0.019 n = n.

Need to find n.

Monthly payment formula is:

`A=(P*i)/(1-(1+i)^(-n) )`

`1-(1+i)^(-n)=(P*i)/( A)\\1-(1+0.019)^(-n)=(18000*0.019)/( 750)\\`

`1-(1+0.019)^(-n)=0.456\\-(1+0.019)^(-n)=0.456-1\\(1+0.019)^(-n) = 0.544\\-n * ln(1.019) =ln (0.544)\\`

`-n * 0.018821754241 =-0.60880603213\\n= 32.34 months`