# 1 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.

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1 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.

2 Approaches…Approaches… Loan problems can be worked two ways: 1.Create a Table… 2.Work problems in the same manner we’ve been using…

3 Perspective … Lender is indifferent between loan payments and investing loan amount at interest rate. Σ Payments = Interest Paid +(Beginning – Ending Principal) PW of Loans = PW of Payments

4 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)

5 Problem 1 You 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.

6 Problem 2 You wish to payoff the loan at the end of 2 years after making your second loan payment. How much do you owe?

7 Problem 3 A student borrowed \$5,000, which she will repay in 30 equal monthly installments. After making her 25 th 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?

8 Problem 4 A 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.

9 Problem 5 If 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)

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