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LoansLoans•When we calculate the annual payment of a loan (A), the payment is actually composed of interest and payment on principal.

•The mechanics are best shown through an example.

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Approaches…Approaches…

Loan problems can be Loan problems can be worked two ways:worked two ways:

1.1.Create a Table…Create a Table…

2.2.Work problems in the Work problems in the same manner we’ve been same manner we’ve been using…using…

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Perspective …Perspective …

Lender is indifferent between Lender is indifferent between loan payments and loan payments and investing loan amount at investing loan amount at interest rate.interest rate.

ΣΣ Payments = Interest Paid Payments = Interest Paid +(Beginning – Ending +(Beginning – Ending

Principal)Principal)

PW of Loans = PW of PaymentsPW of Loans = PW of Payments

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Create a Table…Create a Table…With the following column

headings:

• Year or payment number• Outstanding principal• Payment• Interest payment• Principal payment• Balance Remaining

(next term’s principal)

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Problem 1Problem 1You borrow $1,000 to help pay for rent, food, and books. It is to be repaid in 3 equal, annual payments starting one year from now. Interest on the loan is 12% per year, compounded annually.

Determine the amount of the loan payments, and the corresponding principal and interest amounts in each payment.

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Problem 2Problem 2You wish to payoff the loan at the end of 2 years after making your second loan payment.

How much do you owe?

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Problem 3Problem 3A student borrowed $5,000, which she will repay in 30 equal monthly installments. After making her 25th payment, she desires to pay the remainder of the loan in a single payment.

At 12% per year, compounded monthly, what is the amount of the payment?

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Problem 4Problem 4A company has obtained a $10,000 loan at an interest rate of 12% per year, compounded annually. The loan requires $500 payments at the end of each of the next 3 years (starting one year from now).

Determine how much must be paid 4 years from now in order to payoff the loan.

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Problem 5Problem 5If you have an interest-only loan, your regular payment only covers the interest on the original principle, and the final payment covers the rest.

If you had an interest-only loan for $8 000, determine how much must be paid at the end of 4 years and at the end of 8 years from now in order to payoff the loan. Assume 8% APR, compounded yearly.

What does the cash flow diagram for an interest-only loan look like? (term)