Discussion Overview
The discussion revolves around calculating the breakdown of three equal annual repayments for a $3,000 loan at a 9% interest rate compounded annually. Participants explore how to determine the interest and principal components of each payment over the repayment period.
Discussion Character
- Technical explanation
- Mathematical reasoning
- Debate/contested
Main Points Raised
- One participant seeks clarification on how to approach the problem of three equal annual repayments, expressing familiarity with compound interest but confusion about the repayment structure.
- Another participant mistakenly suggests that three payments per year are involved, which is corrected by others who clarify that there are three equal annual payments.
- Participants discuss the calculation of interest and principal payments, with one proposing a method of calculating interest on the remaining balance after each payment.
- Concerns are raised about the total amount paid over three years not matching the compounded loan amount, leading to questions about the annual payment structure.
- A participant provides a detailed breakdown of calculations for each year, including the principal and interest amounts, and seeks validation of their approach.
- Another participant agrees with the breakdown but notes that if fractions of pennies are ignored, the final balance may not be exactly zero at the end of the repayment period.
Areas of Agreement / Disagreement
Participants generally agree on the method of calculating interest and principal payments but express differing views on the implications of rounding and the total amount paid versus the compounded loan amount. The discussion remains unresolved regarding the exact handling of fractional amounts in the calculations.
Contextual Notes
Participants highlight potential issues with rounding and the treatment of small discrepancies in the final balance, indicating that these factors may affect the accuracy of the calculations.
how would you do it annually instead of 3 years?