The manager of a manufacturing company knows that they will need a new machine in one of their factories. The new machine will cost them $12,500. The manager has determined that they can afford to pay 10% of the cost of the machine in cash. They can then finance the rest through a credit union. The credit union will charge 2% per year compounded monthly. How much are their monthly payments for 4 years

8720Answer:

$244 per month

Explanation:

Monthly payment includes the payment of interest and principal as well. We cannot simply divide the total amount with numbers of payment because there is compounding interest which is behaving differently.

As per given data

Total machinery cost = $12,500

Advance payment = $12,500 x 10% = $1,250

Financing amount = $12,500 - $1,250 = $11,250

Use following formula to calculate monthly payment.

Loan Payment per month = r (PV) / 1 - (1 + r) ^-n

r = rate per period = 2% per year = 2%/12 per month

n = number months = 4 years x 12 months per year = 48 Months

PV = present value of all payments = $11,250

Placing values in the formula

Loan Payment per month = 2%/12 ($11,250) / 1 - (1 + 2%/12) ^-48

18.75

Loan Payment per month = $244 per month

The monthly payment is $ 244.07

Explanation:

The monthly payment van be computed using the pmt formula in excel, which is = pmt (rate, nper,-pv, fv)

rate is the monthly rate on balance after the down payment which is 2%/12=0.001666667

nper is the number of monthly payments required in 4 years i. e 12*4=48

pv is the amount to be paid after deducting the down payment of 10%

$12,500 - ($12,500*10%) = $11,250

The future value of the repayments is not known, it zero.

=pmt (0.001666667,48,-11250,0)

pmt=$244.07