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Comprehensive Guide to Loan Payments: Calculations, Examples, and Interest Implications

This guide provides an in-depth analysis of loan payments, detailing how annual payments are structured around interest and principal. It features practical examples illustrating how to create payment tables and calculate outstanding principal, interest payments, and balance remaining. The document covers various loan scenarios, including equal payments over time, payoff calculations, and interest-only loans. Ideal for students and finance professionals seeking to grasp loan mechanics and cash flow implications. Equipped with tools for accurate financial planning.

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Comprehensive Guide to Loan Payments: Calculations, Examples, and Interest Implications

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  1. Loans • 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… • Loan problems can be worked two ways: • Create a Table… • 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 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?

  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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