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10-8 Credit CH 10]

Calculating the Monthly Payment. Merchants selling on with an installment plan add
an accrued interest charge to the unpaid balance; Interest + Principal yet paid. The buyer
makes regular payments and reduces the unpaid balance, debt, with each payment. A
nominal rate is a the stated interest rate, but the actual rate is generally higher, and is
termed the annual percentage rate, or APR. The amount of the monthly payment is found by
dividing the sum of the unpaid balance and the finance charges by the number of monthly
installments.

Example A: A local super center sells a Nikon D3500 camera bundle that lists for
$978.54. The camera is priced at $438.00, with installment purchase terms
of a 10% cash down payment plus taxes as levied on the purchase. The
unpaid balance to be paid in 10 equal monthly installments. The store
charges 15% nominal interest on the unpaid balance. How much are the
monthly installments?

Solution algorithm: (Cash Price − Down Payment = Balance owed)
$438.00 cash price
- 43.80 deduct 10% down payment
$394.20 unpaid balance (Balance owed)
+ 49.28 interest on $394.20 at 15% for 10 months ($394.20 x 0.15 x (10/12))
$443.48 total amount to be paid in installments
$443.48 ÷ 10 installments = $44.35 monthly installments.

This payment structure will pay off all of the balance and interest due on this time
purchase.
With these types of purchases if there is a de minimis amount, such as ¾ ¢, each
de minimis: too payment would amount to (10 x ¾ ¢ =) 7.5¢ over 10 months, instead of being computed as
trivial or minor to nominal interest, the finance charge may be a stated rate of the unpaid balance. This
merit method of computing the finance charge is usually applied to short-term loans of a few
consideration months. The term of the loan, whether 6 months or 60 months, does not affect the total
finance charge to be paid. The base, the unpaid balance, is simply multiplied by the rate to
calculate the finance charge, and the payment is rounded up to $44.35.

Example B: You have decided to purchase a Canon XF300. This video camera can be
purchased for $3,359 cash or $359 down and 10 monthly payments. The
simple interest finance charge (nominal interest) is 15% of the unpaid
balance. Calculate the amount of the monthly payment.

Solution algorithm:
$3,359 − $359 = $ 3,000 unpaid balance
$3,000 x 15% x (10/12) = $ + 375 finance charge ($3,000 x 0.15 x (10/12))
$ 3,375

($3,000 + $375) ÷ 10 = $337.50 monthly payment

Loan Payment Structures and Payoff
When borrowing money for any purchase the lender anticipates earning 100% of the
interest the borrower agrees to. The thinking is that when a purchase is paid by an
installment plan, a loan is incurred and the presumption is that the consumer (debtor) is
borrowing the finance charges (interest on the debt) as well as the principal. Therefore, the
consumer (debtor/borrower) owes the total of the principal and finance/interest charges. In
some situations, the buyer may decide to pay off the balance of a debt early, rather than
continue making payments for the number of months remaining in the loan agreement and
contract. When this happens, the lender will not earn or receive all of the interest as
stipulated in the purchase and loan contract. Prior to entering into any loan agreement, it is
important for the borrower to ask about any ‘pre-payment’ clauses or ‘pre-payment penalties’
whereby the lender will set a charge to the borrower for paying off the loan early.
It is equally important to know how the payment is divided to pay for both interest and
principal due on any loan. Simply put for every payment made the interest due is paid first
and the balance of the payment not used to pay interest then reduces the loan balance

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