calculating interest

Chapter Six: Calculating Interest

Learning Objectives

  • Ability to solve for the interest paid over varying lengths of time.
  • Demonstrate solving for the principal, rate, or payment.
  • Preparation for upcoming chapters focused on common loan calculations.
  • Examples and guided problem-solving will be provided.

Introduction to Interest

  • Interest is a crucial aspect of borrowing.
  • This chapter focuses on nonamortized loans.
    • Definition: Nonamortized loans are loans where the borrower pays only the interest throughout the entire loan period.
    • The principal remains constant and must be paid in full at the end of the loan term.
    • Commonly found in commercial and investment real estate.
  • In contrast, amortized loans involve the borrower paying both interest and principal, with the contributions toward each changing over the life of the loan.

Nonamortized Loans

  • All calculations in this chapter relate specifically to nonamortized loans.
  • Characteristics of nonamortized loans:
    • Payments remain constant (interest only).
    • Principal is repaid as a balloon payment at maturity.
  • Definition of straight loans: Loans where the borrower pays interest only.

Math Practice: Annual Interest Calculation

Formula for Annual Interest
  • Formula: Principal × Interest Rate = Annual Interest
  • Reminder: This formula applies only to nonamortized loans; it is not valid for amortized loans due to decreasing principal.
Example: Calculate Annual Interest
  • Borrower: Jamie
  • Loan Amount (Principal): $200,000
  • Interest Rate: 4.5%
    • Convert interest rate to decimal: 4.5% = 0.045
    • Calculation:
    • Annual Interest = $200,000 × 0.045 = $9,000

Math Practice: Monthly Interest Calculation

Formula for Monthly Interest
  • Formula: Annual Interest ÷ 12 = Monthly Interest
  • Note: This formula calculates monthly interest owed for one payment, but is not applicable for multiple payments due to principal reduction.
Example: Calculate Monthly Interest
  • Borrower: Lauren
  • Remaining Balance (Principal): $300,000
  • Interest Rate: 4.15%
    • Convert interest rate to decimal: 4.15% = 0.0415
    • Calculate Annual Interest:
    • Annual Interest = $300,000 × 0.0415 = $12,450
    • Calculate Monthly Interest:
    • Monthly Interest = $12,450 ÷ 12 = $1,037.50

Math Practice: Quarterly Interest Calculation

Formula for Quarterly Interest
  • Formula: Annual Interest ÷ 4 = Quarterly Interest
Example: Calculate Quarterly Interest
  • Using Lauren’s Annual Interest: $12,450
    • Calculate Quarterly Interest:
    • Quarterly Interest = $12,450 ÷ 4 = $3,112.50

Other Interest Totals

  • Some scenarios may require integration of both annual and monthly interest calculations.
    • Example of a 15-month loan:
    • Annual interest for the first 12 months + (monthly interest × 3) = Total Interest
    • Alternatively, directly calculate monthly interest and multiply it by the number of months (15).

Example of Calculating Interest

Annual and Monthly Interest on a Specific Loan
  • Real Estate Agent: Matt
  • Client: Amber
  • Loan Amount (Principal): $115,130
  • Interest Rate: 3.75%