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 20% of the cost of the machine in cash. They can then finance the rest through a credit union. The credit union will charge 1% per year compounded monthly.
Required:
1. How much are their monthly payments for 4 years?

 = $212.61  per month

Explanation:

When a loan is to be paid over a period of time using a series of periodic equal installments, it is called loan amortization. Each equal installment is meant to liquidate the principal and the accrued interest.

The amount to be financed by way of loan=

= cost of machine - (20%× cost of machine)

= $12,500 - (20%  × $12,500 )

= $10,000

The monthly equal installment is calculated as follows:

Monthly equal installment-= Loan amount/Monthly annuity factor

Monthly annuity factor

=( 1-(1+r)^(-n))/r

Monthly interest rate (r)

= 1%/12= 0.0833%

Number of months ( n)  in 4 years

= 12* 12 = 144

Annuity factor

= ( 1- (1.000833)^(-12×4)/0.000833

= 47.033

Monthly installment =  $10,000/47.03

= $212.61  per month

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