Question

On April 1, 2018, John Vaughn purchased appliances from the Acme Appliance Company for $1,200. In order to increase sales, Acme allows customers to pay in installments and will defer any payments for six months. John will make 18 equal monthly payments, beginning October 1, 2018. The annual interest rate implicit in this agreement is 24%.Calculate the monthly payment necessary for John to pay for his purchases.

Answer 1

Answer:

The monthly payment necessary for John to pay for his purchases is $88.4 per month

Explanation:

Fixed Installment payment for a fixed period period of time with a specified interest rate is the type of annuity.

According to given data

Present value of appliance= PV = $1,200

Numbers of Payments = n = 18 months

Interest rate = r = 24% annually = 2% monthly

Value on October 1, 2018 = 1200 x ( 1 + 2%)^6-1 = 1,325

Monthly payment can be calculated by using following fomula

PV of annuity = P x [ ( 1- ( 1+ r )^-n ) / r ]

$1,325 = P x [ ( 1- ( 1+ 2% )^-18 ) / 2% ]

$1,325 = P x [ ( 1- ( 1+ 0.02 )^-18 ) / 0.02 ]

$1,325 = P x [ ( 1- ( 1.02 )^-18 ) / 0.02 ]

$1,325 = P x [ ( 1- ( 1.02 )^-18 ) / 0.02 ]

$1,325 = P x 14.992

P = $1,325 / 14.992

P = $88.4